A more serious comparison. I've tried to be objective, but I flick wildly between the two DEs so please forgive any bias...

Aesthetics
GNOME has a very, very slick look, no doubt about it, yet KDE has many beautiful styles available on the internet (say, at KDE-Look.org or APPS.KDE.COM). KDE apps tend to look slightly more uniform, as they all share the same interface guidelines. Compare the GIMP and, say, AbiWord...not much convention there, although they do tend to look slightly similar due to the toolkit.

Speed/Features
GNOME always tends to be slightly faster than KDE (you can test this by timing how long a new kernel takes to compile under each one-GNOME is virtually always slightly quicker), but KDE compensates for that with kickass features that GNOME doesn't have yet, such as desktop blends and multiple wallpapers.

Applications
I'd say that the two environments tend to be equal. Both have an office suite (Koffice/The GNOME Office), both have an iTunes esque program (JuK/Zinf), both have a giFT client (Apollon/giFToxic)...you'll probably be able to find what you need on both.

Ease of compilation
If you get QT binaries, compilation of KDE is ridiculously easy, with simple tarball options available (office, base, libs, games...). GNOME is very hard to compile...or should I say download, as the GNOME distribution is spread over around 50 tarballs, each of which are interdependent. And they wonder why I use the RPMs...

Which should I choose?
  • If you like everything to be infinitely customisable through a great GUI, and like uniformity in your applications, choose KDE.
  • If you like your desktop to be slicker than an eel covered with Vaseline, like it nice and fast and don't particularly care for infinite customisation at the expense of speed, grab GNOME.