It's really dependant on your tastes. The Wii has some really original and fun games, more so than the 360, but the 360 has the biggest game library out of all the consoles. If you like RPGs and FPSs, go for the 360.
If you like Nintendo's first party offerings and some really original titles, go for the Wii. You can't go wrong with either, I have about 20 Wii games, all that I love, with around five or so more that I want, but bear in mind the size of the 360's library pretty much means you wont' be disappointed at all.
Whichever you choose, get the other one as well, it's a good combination for the total they would cost. I do find it funny about the party machine hyperbole. I only have around 3 games that could be good with groups of people, the rest are more solitary or co-op oriented.