Social and Family games goes to the Wii, while Xbox is more for Competitive Gaming even though all of the lag on the Xbox 360 games is unbearable.
This being said, PS3 has Completely free Online Service and NO LAG due to Dedicated servers, while Xbox uses P2P, Player 2 Player, Hosting, which creates even more lag due to multiple connections on one person...
Wii also has Dedicated servers so again... It's all your choice on Games and Console preference.
I say the Wii because you can play the older sega and super nintendo games. Also new releases like DKC Returns, and Epic Mickey? Xbox, I quit paying for gold membership years ago. Don't get suckered into buying more than one 360 because the one before fried. Go ahead and try your luck :]