I would recommend the XBOX 360. IMO, there are many more games that are worth playing, plus the online gaming network is much larger, and if your into that kind of thing that should sell it right there. I have a 360, and I don't even use it to play games in the normal mode, I just play on XBOX Live with my friends. The earlier 360's had an issue with the motherboard failing (AKA "The Red Ring of Death") but the issue seems to have been solved with last few batches. My 360 which was purchased last July, has not had any issues at all, but all of my friends, who bought them when they first came out (2005) have had failures, but MSFT is really good about fixing/replacing them.
I didn't even consider the PS3, because I'm a huge Halo fan, but one of my friends has a PS3, and they say that it was the worst game system that he has ever bought, because the games for it suck.
I do have a Wii, and honestly, I hate the thing. The graphics suck, the games suck, and the way you interact with the game is just plan dumb IMO. I played my Wii once, and I boxed it back up after that first time.
There are plenty of games for little children to play on the 360, like "Viva Pinata" which I think is a great game.
Don