I've used both fedora core 6, mythdora which is myth tv on a stripped down version of fedora, and Ubuntu. It depends what your into.
I like Ubuntu because it's not as bloated as fedora. I am typing on a 400 mhz computer right now with 512 mb ram and the thing flies except for boot up.
Fedora is great for having the majority of the software already there but I don't like yum since it's slow and I hope will some day be able to compete with the speed of apt-get. Although I found installing mythtv went much better with fedora I'm sure Ubuntu is catching up. I heard the latest Ubuntu support most capture cards out of the box.
If you go with Ubuntu I suggest automatix if your looking for support of most media types, players, and some cool tools although the program is in questionable legal standing with some of it's add-ons like DVD support.