I would say go for the xbox 360 if that is what he has his heart set on. The wii, as fun as it is, is only fun for a short while it soon gets stale in my opinion though I'm not a gamer but i do like to play mario kart online every so often and the good thing about the wii is that you don't have to pay a subscription to play online whilst with the xbox 360 I'm sure you have to pay a monthly subscription to play online against other online users.
edit: I would suggest you pay gamespot.com a visit and compare the selection of games that both consoles have to offer and what genres that warrants purchasing the right console for your kids.
Grrrrrrrrr mario Kart. Damn you bullies *waves fist at the mario kart online users for bullying*