It was year 2006 when Wenger got to sign one of these 2 players

Yea, it's Bale and Walcott
He was able to pick just one of these guys, so what do you think? 
Did he right decision?
I personal think Walcott is the player who is longer the "star" of the team.
But last 2 season, and specially in this Bale became better. 
If u were AW who would you sign? Walcott or Bale?

I would rate them equally. 

It would be pretty harsh to say Wenger made the wrong choice.

All Walcott really has is pace... Bale has amazing free kicks, defencding abilites, pace too and a very powerful shot. He also has some fancy skills. AND he if LEFT footed (like me) which is rarer, and most left footers are better,, ,there are many of us though xD

Also consider the fact that Bale started as a full-back. He's slowly become a winger, and now possibly more central, having to learn a new position every couple of years.

Walcott has been training as a winger all his career. 

Probably Bale right now, think he has a slightly better whole package, Walcott is a very good player but his consistency is an issue, probably not aided by the fact Wenger keeps changing where he wants him to play.

BACKGROUND: Liam Brady, Arsenal Legend & long-time Director of Head of Youth Development, wanted both players when he approached Wenger about them. At the time, I think Walcott's stock was higher (probably simply because he was an attacking player) but it rumoured that Brady was a bigger fan of Bale. In the end, Arsenal made an offer for both but Wenger prioritized Theo (he was a big fan of his). 

CURRENTLY: There is not even a question that Bale is the superior footballer at the moment. His projected worth is far higher and he has developed his game at a surprising rate in the past 3 years. Theo Walcott is an excellent footballer as well and it is my opinion that he will continue to grow. He has been criticised heavily in the past for his lack of decision-making and consistency but Wenger has pointed out that usually starts to fully develop at arround the age of 22-23 and he is seemingly being proven right as Walcott has some of the best stats in the premiere league. His finish, intelligence, and overall importance has definitely improved greatly from when he was 16 yo thrown into the media spotlight.

In the end, I believe it is disingenuous and too easy to say in hindsight Wenger should've bought Bale.  Remember, at the time (Jan. 2006) we had Cashley Cole at LB with Flamini (who occasionally played there as well) & Pires as LW.

In the end, I don't think Wenger made the WRONG decision but it would've been nice to also bag Bale. In any case, he has developed very well at Tottenham and sometimes it's better for the league to have talent distrubted around instead of all in 1 team. If Spurs don't make CL this year I every suspicion that he will be off. Perhaps, if they do he MAY put off a transfer.

I hope that helped.

I'm with what Lodatz said, Bale used to be more as a defender back then and AW wanted a winger.