I don't have a PS3, I've never played on one, so I'm clearly biased with my 360. Please take that into account in this post. Someone with a PS3 can make a case for that, I'm not qualified to criticize it appropriately.

Xbox Live Arcade is a great way to build up a library of cheap (average 400 points) games. There's a huge variety too. Board games (Catan), Shooters (Alien Hominid HD, Assault Heroes), rhythm games (Boom Boom Rocket), Puzzle games, and even full games from past generations (Mortal Kombat, Castlevania: SoTN though they do cost more). I've got a lot more XBLA games than I do actual discs.

The rentals and TV shows that come in HD are nice (I never waste money on them though because I don't have an HDTV). Xbox Live is currently one of the few, if only, online distributor of HD content. They have anime too (dubbed, but still).

The genres of games on disc is expanding rapidly. The first game I got with it was Tomb Raider Legend. Short game, but certainly the best Tomb Raider game I've played since 2. MS has also realized their library was a little too centered to the American audience with 1st and 3rd Person shooters, so they've started getting into the j-rpg market with Eternal Sonata, and a few other quirky games, like Katamari.

The demos are probably the best part of XBL. They'll put out a few demos of some anticipated titles, and they're usually about 30 minutes of gameplay. It's a pretty good way to gauge whether you want a title. It's the reason I made sure I bought Bioshock, pre-ordered Eternal Sonata, and decided that 99 Nights was garbage from the poor gameplay and worse localization.

There are downsides to the 360.

There are all the hardware issues. The 360 must be properly ventilated, with plenty of space for airflow around the vents and sides. The ring of death comes from people stuffing the thing into entertainment centers. Not everyone has these problems. I'm still on my first, and it sits next to my tv on a hard surface, well off the ground. Never tilt the console while it's on (why I'm on my second copy of Dreamfall).

The peripherals are not cheap. The controllers are pretty standard cost, and the battery life is great. It's the other things that kill you. If you buy a lot of the HD media (and never delete demos) you'll need a bigger hard drive. The 120 is worth it if you do (my friend got one), but it's very overpriced. The wireless adapter isn't cheap either. Mine works great, but at $100, it's expensive.

Several features don't work outside the US. I'm not sure which, but the digital media is the big one. That's due to asshole licensing laws from the Unites States.