It's all a matter of personal preference, and one largely dictated by to whichever network more of your friends belong.
Facebook has a much "cleaner" look to it, and is better maintained. It's targeted towards a more mature demographic than MySpace.
On the other hand, Facebook is more limited in terms of how you can aesthetically customize your profile. This is seen as both a pro and a con - personally, I appreciate the uniform aesthetic. MySpace is more liberal with the kind of content you can upload, I believe. I'm specifically talking about audio files - MySpace is used by lots of bands, who use the medium to promote their merchandise and tourdates. It's particularly useful for finding out when a band is going to be in your town, because a band can send a message to just users with your zip code, for instance, letting you know which local venue they'll be at.
There's nothing stopping you from signing up for both - it doesn't have to be an either / or thing - but it seems that most users are polarized, one way or another, in terms of preference (although many people continue to use both, regardless).
Since Facebook originally started as an inter-college network, it's mostly popularized by people in their early to mid 20s; but it's also very popular with high schoolers as well, now.
MySpace has been available for anyone to join since the beginning, and includes users of all ages - but it seems to attract teenagers the most.
My personal preference is for Facebook.
And remember to keep privacy in mind. Anything you put in either profile could be read by anyone on the internet. Both services offer different degrees of privacy control. I suggest looking into that.