I'm going to break this down into a few subcategories consisting of everything I can think of.
I'm trying to be objective with this, but also making use of personal experience. Don't hate me, fanboys. I own both.
Performance & Appearance
This is probably something you should look at on a game-by-game basis. You might think that the PS3 version of any given cross-platform game would look better because of its innards. However, the simple fact of the matter is that all too often cross-platform titles don't make enough use of the PS3's hardware (due to it being a little tricky to develop for), whereas titles developed exclusively FOR the PS3 look great.
Case in point: Skyrim. I got it on 360 because it looks better & performs better (the PS3 version had a nasty bug where an increase in save files had an adverse effect on performance somehow; it could've been patched since then).
The thing here is that XBLA uses Microsoft Points, which you can pay for in various ways. I don't buy mine through the console because I can get 'em cheaper online. Doing things this way may result in you getting a better deal when getting a game for 360. Then again, it may not. All down to where you get your points and what the game is.
As you probably know, online gaming on a 360 needs a gold account, which you have to pay for. On the PS3, online play is free.
However, in my experience (MINE, NO-ONE ELSE'S) playing games online with a 360 has been a far more pleasurable experience due to fewer connectivity issues and better audio quality when talking to other players.
Then again, maybe the game in question doesn't have online functionality. As I said before, it depends on the game.
Achievements / Trophies
Do you care about either? Probably not, but it's worth mentioning since this is a factor for some people.
Convenience of download
The old 360 doesn't have a wifi adaptor, so you may find it more convenient to use your PS3's wifi to download the game. If you have a newer 360 model, this point is moot.
Okay, I'm reaching a bit here, but it's still relevant. Despite its horrible d-pad, I prefer the 360 controller. Everybody's different.
So, there ya go. Make of it what you will :)