I love my Xbox 360. We have quite a few gaming systems (Xbox, Xbox 360, Game Cube, Playstation 1(I think...), SNES, Gameboy Advance SP, GB Color, and Nintendo DS) and it is by far the best. We've hauled it places, and we've had friends haul their systems over as well. We've never found it to be a hassle, and we love playing together. Personally, I love the graphics, particularly when you have it plugged into a HD TV. (for example, while playing Oblivion with the Shivering Isles expansion pack, the room made of butterflies. To see that in HD is absolutely awesome!) We do not have a Wii, but I've played one quite a bit. Although I recognize the awesomeness of the motion sensitive stuff, I don't like it. It doesn't work for me, I'm just not coordinated enough...
If you have friends coming over every day, then the Wii is for you. It is kinda true that it is mainly for families and girls, but there are lots of FPS games, like Resident Evil, which was really fun for me. The Wii is also built for multiplayer and party games, like Mario Party and SSBB, and it also offers rpgs. Many GC games are being improved and the sequel to those GC games end up for the Wii these days, so the Wii is for those who still want to hold onto their GC games, and experience a whole new way of gaming too.