Xbox does have much more games, but I'm a big fan of the ps3. It has all the really good games, and some great games that xbox doesn't have. Xbox has more games but ps3 has more diverse games imo. And if you get a backwards compatible ps3 you can play ps2 games, which are amazing.
With the xbox kinect and the playstation move coming out, I actually think the ps3 will do better. The kinect is an impressive piece of technology but there's really no point buying it since there are really no games for it. I've heard the move has some great games, but I don't have one so I'm not 100% positive.
I personally like the ps3 better, though it's more expensive.
If you do decide to buy and Xbox, don't ever buy one used. As you have probably heard, Xboxes, especially older ones, but newer ones as well, have issues with soldering, causing the infamous "red ring of death." If an Xbox red rings, it's pretty much dead forever, but if you heat up the motherboard it will reflow the solder you can make it run for another month or so, and you can do it again a few times but at best you can squeeze out about 3 months. I used to work in game console/repair place and we used to buy red ringed Xboxes for cheap and reflow them, and sell them as used Xboxes, knowing full well they will only work for about a month before they red ring. Glad to say I didn't keep that job for long.
PS3s on the other hand, last for ages. The only issue I've ever seen with a PS3 is a disk reader going bad, but that has a pretty equal chance of happening on any console. Also PS3s play blue-ray.
On a side note about the kinect, despite not having any games, the kinect is a lot of fun to play around with. It uses a USB so if you have some computer skills you can hook it up to a computer and hack around with it. Fun stuff.
Another fun fact, both the Xbox and the PS3 have NETFLIX, which has all of Buffy on it.
Oh oh oh, I forgot to talk about the DS, the DS is amazing. Get the original, not the light or dsi. I hear the DSi isn't great, and the DS Lite is fine, but the original is built like a tank and will last forever. I've lost count how many times I've dropped mine from fairly large height, and it was fine, until I lost it on vacation. I was super upset. And it has a great variety of games. If you love fun, playful, silly games, you will love the DS.
Anyway, sorry to babble on, good luck with your new console.