There are a TON of opinions out there on this topic, moat of which are way more "hardcore" than me and get into all the technical factors... but here is how I came to choose the Xbox...
Factor 1 - cost
A quick look at the consoles on amazon as a typical retailer shows the following:
Xbox 360 with 60gb HD (the standard version) - available from 199 Euro
Playstation 3 with 80gb HD (standard version) - available from 330 Euro
Winner: Xbox 360

Here is where you can get into near religious discussions if you go around the internet... Basically my opinion is that they are pretty similar. Most of the side by side comparisons look almost identical to me. Here area a couple I pulled off of google image search on popular games. (from techeblog.com and maxconsole.net)


Winner: DRAW
Factor 3 - Hardware
Another tricky one. I would say there are two parts to this as well. Hardware design and hardware quality. I am going to have to give both to Sony on this one. Not that the Xbox is particularly ugly, but the glossy black PS3 really does look good in the living room.
The PS3 also includes a blu-ray player, which as a standard def TV owner is not interesting, but it is in there.
Xbox also had pretty well documented catastrophic hardware failures on the first generation of consoles, but they are well past those problems now.
All things considered though...

Factor 4 - Games
Basically, all good games get released on both consoles. There are a couple of exclusice titles, but not that many really. Exclusivity is mostly timed these days anyway, so at the worst it means you may have to wait a bit to get a certain game on your console.
Cost of games is basically the same for both too.
Winner - Draw
Factor 5 - Community
Here was another biggie for me. Xbox live is awesome. That is it. I plugged in my Xbox and within the first 5 minutes, I was chatting with Mike Starr, who also happened to be online. Xbox Live lets you play with friends, chat with them, and just kind of do stuff together. You can see if the console is turned on and what your friends are doing, decide if you want to join them or invite them over to do stuff with you.
Of course, what made that more compelling for me was how many of my friends have an Xbox already...
Gord
Mike
Jay
Dave
and a few others....
I know PS3 has recently launched a similar service, but it is by all accounts not as good as the Xbox live one. Also, I only know one other person with a PS3. Much smaller potential for fun...
Winner - Xbox by a mile

Get an Xbox, join the crowd. My gamertag is Frazamagorf, feel free to add me anytime.