I think either way there will be more then enough great games to play. A lot of people would probably try to say you cant get 'serious gamer' type games with a wii, but nintendo actually generally does a good job of having a variety.
The main thing is just the controls I think. After all, controls can make or break a game. So, if you like the wii remote then go for it. If not, stick with the traditional controller offered by the 360.
You can take a chance with the Wii, hoping that it might get a few games that more "hardcore" gamers will appreciate. If you're a casual gamer, I'd say this is the system for you.
360 has a wider variety of games right now. There are a few games that I'm interested in that are exclusive to the system. Check out the upcoming games to see if you're interested in them. You'll have to worry about the "red ring of death", which will eventually happen. Microsoft will give you a three year warranty though.
I'd wait to buy either system if I were you. Wii doesn't have any games that appeal to me and I'd wait on Microsoft to see if they put out a non-faulty system.