I've done a little with MythTV, so I'll stick my nose out here.
The backend is where everything is stored. There will be a MySQL DB running with pointers to the files on the backend system.
The frontend won't need a huge drive; 20GB should be ok - especially if you are going to run a specialized install (like Knoppmyth).
The backend needs as much space as you can give it. I have a 40GB primary drive (OS and temp files) and an 80GB storage drive in my main MythTV box - and I still can't keep EVERY episode of the Simpsons on it.
This (of course) also depends on your settings and if you're transcoding to another format....but that's a story for another time.