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. :)

There is no point of comparison between the 2009 matches and the 2012 ones.. in 2009 referees played a significant part while in 2012 luck and a solid defence was the main factor.

Ive never seen a team get as lucky in any stage of the UCL as Chelsea in 2012 but Ive also never seen a team getting robed as bad as that Chelsea from 2009...

@Lodatz i didnt read your comment, i told you, no need to argue with you dont waste your time and mine.
@Tuanis, i agree for that. But Barça had nothing with the ref, it was the ref mistake why hating on Barça ?

@tiki: you didn't read it, but felt the need to reply to it?

Good one. So mature.

Holy sh*t, even my "Why can't we be friends" video was removed. Stay classy, FR.