So, I decided to do some research, just to see for myself how dominant Barcelona have been in the modern era, and how they have fared against both domestic and foreign competition (and who that competition has been). Here's the data I collected, starting in the 2003/2004 season, for reasons I'll explain shortly. It details Barcelona's performance record against the traditional 'Top 4' of the Premier League, and then also their performance against Real Madrid, as Barca's obvious and closest domestic rival.

I broke the data down further, into two 'eras', as well, to illustrate the influence of Guardiola. As it happens, the two biggest game-changers in European football happened at the same time: Roman Abramovic taking over ownership of Chelsea, and Frank Rijkaard being appointed manager at Barcelona; the 2003/2004 season. As such, I have termed this first period the 'Abramovic era', counting the 2003/2004 season up until the end of 2011/2012.

For the second era I have narrowed the data down even further, to account for the arrival of Pep Guardiola at the helm of Barcelona, and their subsequent rise to dominance in football. For obvious reasons, this is the 'Guardiola era', accounting for 2008/2009 until the end of 2011/2012.

As we can see from the table, in the Abramovic era Barcelona have fared well against the Premier League clubs; gathering a 38% win percentage, and a 57% record of being victorious in knock-out situations (over the course of two legs). However, they have not had it all their own way, as Manchester Utd, Liverpool and Chelsea (twice) have all managed to knock Barcelona out of the Champions League, and some of the KOs against PL opposition happened in the same season (for example: Chelsea and Manchester Utd in 2009, and Arsenal and Manchester United in 2011). In particular, they have struggled against Chelsea, and the Blues even have a higher win percentage between the two clubs. All three CL Final wins were against PL opposition, but it's also true that of the 5 other seasons in the Abramoic era, they were knocked OUT by PL opposition 4 times. 

As for Real Madrid, they have not managed to do as well as the PL clubs, over the balance of the last 8 years; Barca having a 44% win ratio against them in all competitions, and dominating with 47% in La Liga especially. However, it should be noted that the Copa del Rey has seen a very balanced battle for supremacy between the two giants.

In the Guardiola era especially, things start to look even better for Barcelona, with a slightly higher win percentage against the Premier League, and 80% of the KO victories. It should again be noted, however, that Chelsea have proven to be Barcelona's biggest obstacle; in fact, Barcelona have never beaten Chelsea in a single match, even during the height of Guardiola's power. Two victories against Manchester Utd, and twice knocking out Arsenal, however, make it clear that Barcelona have reigned supreme overall.

Against Real Madrid, the success rate has been even more ridiculous, with a 75% win ratio in La Liga, and a 57% ratio overall. Again, the Copa del Rey has been evenly balanced, but with such a huge margin between the teams in the league, over the course of the four years, Barcelona have clearly been the better team, by some distance.

In conclusion, then, there is no arguing that Barcelona have been the dominant club in Europe for the last 8 years of glorious football, even more so in the last 4 since Guardiola's appointment, but they've faced some stiff competition for it, and as we can see from the data, the greatest rivalry to Barca's dominance has not been Real Madrid, but the English Premier League, and that's about even.

Hope this is interesting to others. Just wanted to share. :)

Long live the English Premier League! & England :) Very nice mate, I like Barcelona but the Uefa is kinda ruining it for me I used to support them in spain till 2009 moment.. I don't know what happened to me i just felt like someone robbed my house and the police didn't give a damn, in fact they were the one that robbed the house so there was no hope. this is why i stopped supporting them in spain.

Youd be interested to know that in the Guardiola Era Barcelona had the following record:

La Liga
Played-152  Wins-116  Draws-25  Loses-11  Goals For-412  Goals Against-109
Champions League
Played-50  Wins-30  Draws-15  Loses-5  Goals For-117  Goals Against-43

Those are some incredible results over 4 years. The fact they won 75% of La Liga games and 60% of Champion League games is off the charts. Managed 4 semifinals in a row and 2 final victory.

Very well organized !! .. It is clear Barcelona were the dominant force in Football during these years.

I won't lie, I came here to check Barcelona's record with Chelsea :P. I also don't think any manager will be able to achieve what Pep has in 4 years with Barcelona. It's remarkable!

Well, Madrid seem to be improving everyday. The last five Clasicos ended.
Barcelona wins - 1 (3-2 in the Super Cup)
Draws - 2 (2-2 in the league, 1-1 in the Copa del Rey)
Real Madrid wins - 2 (2-1 in the league and 2-1 in the Super Cup)

Isn't the Spanish Super Cup basically their version of the Charity Shield...?

But yeah, Mourinho's arrival has brought about some parity in their direct results; will it last after he's gone?

@Dynastian98
I wont argue that Mourinho many times managed to get a great result from barca(win or tie) but i dont think that the criteria for that is only the last 5 games.
No offence of course.you how much i estimate you ;) 

I know. We are awesome. :)

I had forgotten about this. I think the only updates which would be needed are the Clasico results.

@AlexBatak Your saying that one year you miss out on the champions league becaues of one bad call and now your pissed off at Barca? Barca beat Manchester United so many times, and so has real madrid as well as plenty of other clubs, it doesn't mean that I won't support them. You can't blame Barca for a shitty call. Yes they are happy because they got into the final, who wouldn't be? Yes I hate to see Manchester United lose. Yes, I love to see Manchester United win. AT the end of the day, it is just football, and the team that got lucky, and played the best is the team that takes the glory. You can't hate on the success of other clubs for getting lucky, or playing better than your team. I get as much pleasure watching Real Madrid win as much as I like to watch Barcelona. Yes, real did get us out of the CL bcause of a shitty call, but that is not their fault for having a better team, and getting lucky with the referee's decisons. AS long as they are not diving or cheating I don't give a damn, because at the end of the day the best or the luckiest team wins, and you just have to accept it and live with it, even if the lucky team is not your team. Therefore I really don't know what your pissed off at Alex. Phew that was a mouthful. lol

^The thing is... United got trashed by Barcelona in a fair way, Chelsea got robbed and that night will be remembered as one of the biggest upsets from Uefa and refereeing (dont know if upset is the right word to describe it). I would be pissed at barcelona as well if that happened to us, that year Chelsea could have gone to the final and United could have won it! jk, but that one game can piss the hell out of many fans for the rest of their lives, that kind of games with that much controversy are not played every day.

Oh and lodatz, great research btw...

@Tuanis i guess you are right when you put it that way.

Thanks Tuanis for explaining :) @messi6511 The UEFA clearly didn't want another Manchester United vs Chelsea Final 2 times in a row. I wouldn't be mad if it was one bad call but it wasn't 1 nor 2 or 3. We deserved to win that match and we were attacking nonstop. I can never forget that match and I was so calm watching it because we were dominating and to not go through was not even thinkable in that game. Anyways, That's in the past now and we got our revenge.

Edit:
Im not gonna hate at Inter because they had an offside goal and they beat us, thats not fair.
In 2009 we got Lucky as Chelsea were lucky in 2012, ref mistakes has nothing to do with Barça players or direction...
I hear a conspiracy against Chelsea by UEFA, well im not sure they gave ref the right to cheat in front of millions,because its not a stupid qualification game, its a semi final game...
Well we got Unlucky in 2012, Chelsea would have never past us 9 times out of 10 that year, we were dominant in both legs creating dozens of chances in both games.
The good defense, an incredible Cech, the cross bar and Karma made us loose, when we did everytthing to win.
Even Ramirez goal was inexpected as it was their only action......
I understand that you felt robbed in 2009, but we needed to score to qualify and we did it. We were at 10 men on the pitch and at Stanford bridge, your team could have controlled the game. Instead of that, they went defending instead of try to kill the game.

But i admit the fact you deserved to pass over us in 2009 considering the circumstances.... That was a big hold up.
2009 is a great memory for me as 2012 is for Chelsea fans, you can think what you want about conspiracy about English teams, personnally i find it impossible. But DONT HATE at my team publicly they are not UEFA. ( Im not talking specially to Alex, he seems to be a nice fan but just go on highlights and look to Chelsea fans comments on Barça).

The phantom goal of Liverpool was a bigger mistake as they qualified without scoring, which is incredible and different than Barça case, as Iniesta needed to score a VALID goal to qualify us....

If Chelsea deserved to play 2009 final, we deserved to play 2012 final. Instead, we won in 2009 and they won in 2012... I think both fans of both sides needs to understand how others felt in both confrontations.

@Tiki-taka How on earth you compare our match in 2012 with 2009? where as we were playing 10 players and won at home and drew away without any cheats? Barcelona's players were diving and pulling players and using their hands all game in 2009 match mate. I'm not hating on Barcelona I'm just stating the obvious to what I felt about it, nothing more.

Why don't you think about it as Barcelona were not using their defense at all and that's why they got punished by the aging blue lions? Or were just very bad at defending? I think they forgot that defending was part of the game. We were playing counter-attack style while Barca were playing their tiki taka and wasting their time instead of scoring a goal.

Drogba dived as well, and the defense made some dangerous fouls against Messi to intimidate him, dont forget he was injured 2 times by Chelsea players, his 2 first injuries...
Yeah there was some bad atitudes by both teams, i dont like when Busquets dive too, but Chelsea were not the best at fair play too...
We have a polarized battle : Skills vs Power, so diving and dangerous tackles would be always expected in those important games.
Im not making a big deal of it, but a one-side view can be combined to the other side view to make an neutral objective view.
I felt the opposite as a Barça fan, we have the kind of players that can not be accepted in France and England youth centers, short thin and not Athletic, but its the price to pay to produce such a magicians like Iniesta.
And i dont like playing Chelsea because they concentrate just on physical impact against us, and sometimes its exagerated for some players ( imo as a Barça fan ), but i know that others appreciate other styles than my favourite style and thats what im talking about.
I can try to be the most neutral toward those debates, but others should do the same to converge on ideas.
I understand how you felt in 2009, i cant say it was fair result for you. We qualified knowing that the rival deserved to qualify as well.
And try to understand how i felt in 2012, nobody talks about the first leg of 2012, who was completely dominated by Barça, we had plenty of chances and we got incredibly unlucky with an English style ref ( not claiming anything ).
The 1-0 was completely unfair if you remember, all this to tell you that as passionate fans, we see better what deserves us....

Its amazing to see how the memory of events changes depending on wich side you support, i can understand the one-side view of a Chelsea fan as he should understand the one-side view of a Spanish Barça fan. Both dont live the game the same way.

For example in 2012, i remember more this game than the second.

In 2009 Chelsea were cheated out of 4 (5, even) penalties, to put the tie to bed.

In 2012, after going down to 10 men (losing their captain and ONLY CB as a result), Chelsea out-played Barcelona by nullifying their attack, and getting the two best goals of the game on the counter-attack.

Anyone who denies this is biased, and ignorant.

^If only you weren't a Spurs fan... :P

"Why don't you think about it as Barcelona were not using their defense at all and that's why they got punished by the aging blue lions? Or were just very bad at defending? I think they forgot that defending was part of the game. We were playing counter-attack style while Barca were playing their tiki taka and wasting their time instead of scoring a goal."

This is it, in a nutshell. The simple fact is: Barcelona's football was inferior to Chelsea's football. But you will never, ever get a Barca fan like tiki_taka to admit it, because to admit it would be to admit that the 'best team in the world', playing the 'best football in the world', came up short against the PL's 6th best team, who were down to 10 men and already ravaged by injury.

It's that bias, that stubborn refusal to just accept reality, that is the reason we we have to keep having all these constant arguments about both Barcelona, and about the leagues. Any objective viewer can see the difference, because it's so obvious. It takes enormous bias and a refusal to admit error that keeps this cycle going.

I mean, when you consider the fact that PL teams have knocked Barca out of the CL 4 out of the 6 times they've lost, and that while Barcelona are getting stomped by Bayern, PL teams are beating Bayern, it takes a real bias against the PL (or a ridiculous amount of bias towards the Spanish league) to keep arguing this.

It's just sad, by this point.