I run Debian.
SFAICS it largely boils down to the method of package management. It's pretty much a two horse race: Debian (and derivatives like Ubuntu) use apt and Redhat-based distributions use rpm. From my limited experience of running both, Debian's package management seems more reliable, and simpler to begin with, but potentially more powerful in the long run. Debian also port to many more architectures, including arm.
The rest of the differences between distros can be 'tweaked out' to suit - which window manager, and that sort of thing - kind of non-essential issues.
Dunno if you care much for the politics, but Debian are the most puritanical over open source software. I'm definitely with them in spirit, but sometimes you find yourself saying "I just want this hardware working, without a great political debate with the manufacturer! Just gimme the closed source binary driver!" On the flipside, Ubuntu can sometimes seem the opposite: a bit too commercial.. A bit Windowsy, with a dictatorial figurehead like some Linux equivalent of Bill Gates (Mark Shuttleworth).
Go with Debian. My 2c! Although at the end of the day, 99% of the distros are identical!
cheers, a