Which media center OS should I use?

There are a number of options.  MythTV on lilnux is a really good option - I think it is the most mature.  Until tomorrow it is completely free.  After tomorrow you have to pay a tiny amount of money for tv listings.  This isn't a payment to myth, but someone has to provide accurate tv listings (the cable companies don't just give them away unfortunately).

MythTV's web site is http://www.mythtv.org/

You can install mythtv on just about any linux system.  There are RPMs available for Fedora or Redhat.

There are also more pre-build out-of-the-box mythtv soltions such as mythdora  at http://www.g-ding.tv/ which is fedora set up for mythtv.

For comercial systems Windows Vista Home Premium and Ultimate have Media Center with them.  This is probably the easiest to use, really easy to set up, etc.

I'm a long time mythtv user and media center really is quite awesome.  They both do some things better than others.  Vista is insanely easy to set up.  Vista Media Center's interface is a LOT cleaner, a lot easier to hook up to a TV, but a lot harder to schedule and manage recordings if you have more than a few shows you watch.  In typical MS vs. Linux fashion, MS makes it simple by saying "record this show" and thats about all you get other than the ability to tell it not to record reruns.  Myth will let you say only do it at this time on this channel, only when it is sunny outside, and only if Michigan is ahead by more than 10 points.

It also matters which TV card you have.  If you have something that is nicely supported by MythTV like a hauppauge PVR card, and you kinda know how to set up a linux box, then MythTV might be a great option.  Otherwise, Vista sure is easy!

MythTV also allows lots of plugins like nintendo emulators, etc.... but some of them are pretty buggy and hard to use (especially mythmusic which is just horrible).

Vista has this nasty digital rights problem though.  Just the other day it told me I couldn't record some series because the distributor doesn't want me to.  MythTV recorded it just fine.  Of course I just decided to stop watching that stupid series if they want to play that game - it wasn't very good anyway.

If you have vista and a machine to use as a dvr already, then vista is a good option.  But I sure has heck wouldn't go out and buy a new machine to run vista on just to put it behind my tv.  Vista wants a fat processor and 2gb of ram, and I'll be darned if I want to go buy something that cool and put it behind my tv.   Mythtv runs great on a 1gb p3 with 512mb of ram - a machine that would otherwise be completely useless.

One last note on extenders:
Vista machines can share music and videos.  Pretty nice if you have a vista machine in your office and want to watch stuff on the remote machine.  An xbox360 can also be a front end.  Picking up a basic entry level xbox 360 actually makes an affordable addition to be able to watch my recorded programs in my exercise area, rather than buying a whole new tivo-type setup.

MythTV is really easy to make front-ends.  I have a 1ghz p3 with only 256mb of ram in my basement tucked away doing the recordings.  I then have 2 more 1ghz p3 machines, each with a 8gb hard drive (could even boot from flash or a cd rom and have no disk at all) as front-end systems that connect to the machine in the basement.  So my whole DVR network is run on otherwise throw-away PCs.  Another nice thing about having the backend in the basement is that the machine in the bedroom is only booted when I want to watch tv - no leaving a noisy computer on 24/7 when I'm trying to sleep, or having it come alive at 3am to record a program.

Good luck.  Its a hard decision.  It all boils down to what  you're comfortable with, what hardware you already have, how much money you have, and if you want to be "cool" and have a linux dvr.