Disclaimer: I've worked as a writer/designer on some 360 games (such as Ghost Recon: Advanced Warfighter), and some PS3 games (most recently, SOCOM: Confrontation). But I've got both consoles, and even though I'm currently working for a Sony subsidiary, as a gamer, I try to be impartial.
The 360 had a nice head start, so there are lots of games to choose from, and plenty of lower-priced Greatest Hits titles as well. Whether you dig single-player, multiplayer adversarial, or co-op, you have many options. Xbox Live is easy to use and fun to play around with. There are some really great games on the system -- I'm currently enjoying Prey, Quake 4, Gears of War, Oblivion: Game of the Year Edition, and Orange Box.
The PS3 doesn't have as many games to choose from, but right now I'm playing The Darkness (horror-action FPS) Warhawk (flight combat), Resistance: Fall of Man (really enjoyable horror-war FPS), and Armored Core 4 (mech combat). I have Heavenly Sword, Lair, and Eye of Judgment, but haven't had a chance to play them yet. Upcoming PS3-exclusive games that I've heard good things about include Unreal Tournament 2007, Killzone 3, Devil May Cry 4, Gran Turismo 5 Prologue, Metal Gear Solid 4: Guns of the Patriots, and SOCOM: Confrontation (which has amazing dialogue, or so I hear...
). I don't know much about PS3 online, but now that a buddy of mine has one, we're probably going to do a bunch of online gaming in the near future, so I may post my findings then, if you like.
I love my Wii, but I can't sit there and play a Wii game all night the way that I can play Prey or The Darkness for hours and hours. Zelda was okay, but I've been playing for a while and I still haven't seen much action. Mainly cute villagers. That I can't kill. Grumble...