All the consoles have their advantages and disadvantages. It'd be harder to choose between PS3 and XB360, but since you want to know between XB360 and Wii, it's a little easier
XBox360
Pros: high def, media connectivity, much higher quality graphics. optional hd-dvd add on, console doubles as dvd player.
Cons: hardware reliability, console is *very* loud, much more expensive than wii
Wii
Pros: Nintendo as a first party publisher, built in wi-fi, unique interface, cost much lower, virtual console
Cons: graphical quality much lower, unproven third party support
If you like the highest graphical quality and "mainstream" games, XB360 is an easy choice.
If you like different games and can't live without nintendo's awesome first party lineup, Wii is the choice.