What's the difference between KDiff3 and Kompare?

Should I use one over the other?

Kdiff3 is a three-way diff application, so it can be used as git difftool. It’s useful for instance when you need to rebase. You see the original, your changes, and the remote changes, hence “three-way”.

The UI seems rather outdated, and it seems to be geared for keyboard use.

IIRC Kompare is not three-way, only two-way. It can’t be used as git difftool but it can be used for things like checking the difference between two whole folders, which I’ve used myself to identify faulty configuration files in the past.

I remember liking its UI better and it being nicer with the mouse, though it’s been a while.