As a guy who used to buy almost every console out there, back when it was still Nintendo VS Sega VS 3DO (lol!), and then suddenly living in a world where you really have to spend money wisely and only pick one console if that's your main form of entertainment, I'd say I do not like the idea of relying on console exclusives just to make one console better than the other.
Let's say you're just the average guy who can only support one's gaming habits on one game console. What if an exclusive game came out for the other console, and that game is really really good and looks fun, and as a gamer you just want to play it as well? Well you can't. You either go to a friend's house who has the other console to play it if he ever buys it, or you just watch videos of the game on youtube or justintv just to satisfy your interest in the game. You can save up cash to buy the other console, but then again, are you really willing to let go of $300 just to be able to play another $60 game which you'll probably get bored of in a few weeks or months?
Of course, every game company has a right to create exclusive games. Just look at Mario and Sonic, they were the flagship bearers for Nintendo and Sega respectively. Both characters represented their console's abilities very well in their games. Mario was about having fun in a carefree and cute world full of funny and pleasant environments and enemies, while Sonic was all about being "cool" and "rad", blazing through levels designed to make you feel like you're a moving roller coaster animal. It was very easy to decide as a gamer which side you were going to take because you just picked which character you related to the most. The good thing about this was no matter if you chose Nintendo or Sega during their SNES VS Genesis years, you still got to play every other interesting game that came out because going multi-platform was the norm.
I still remember that old issue when Nintendo refused to put blood in their SNES version of Mortal Kombat, while Genesis has no qualms giving gratitious blood, even providing gamers the "D,U,L,L,A,R,D" code to give the maximum effect of Mortal Kombat on the Genesis. Still, even though games had differences due to following the company's image (Nintendo's supposed to be family friendly), as a gamer, you were still able to play Mortal Kombat on the SNES, you were not completely locked out of the experience, especially since a few Game Genie codes (a device used to cheat on both SNES and Genesis) remedied the no red blood problem of the SNES.
Then came the new consoles, the Xbox 360 and PS3. I remember I already wanted the Xbox 360 at the start because of what I read about it. I also found out that it had an exclusive game to it called "Dead Rising", and coincidentally I'm a zombie lover! Then it hit me, what would happen if for some reason, my first choice was the PS3, and this Dead Rising game was only for the Xbox 360? That's the time when I realized that for single console owners, console exclusives wouldn't be great at all. Just imagine, what if your choice of game console had this one great game exclusive, and then all of a sudden, the other console kept churning out their own great console exclusives that you want to play, but your system has stopped creating their own console exclusives? You're stuck with 1 vs their many.
So as much as possible, in my personal choice, I'd rather have the common multi-platform games instead of having exclusives. We already have the DLC system set up for this, and they're already doing it. Having game console extras is fine in my opinion, just like how the PS3 version of Batman: Arkham Asylum had Joker as a playable extra. It didn't block out the Xbox 360 and PC gamers from enjoying the game normally, it only gave the PS3 owners a little something to cheer about.
I believe that the greatness of a console should not mainly depend on what "exclusives" it gets, but on the actual performance of the system itself when it runs games. It should let the gamer immerse him/herself as much as possible into whatever game is being played, without being distracted by technical details.
