I think your decision should depend on:
How you intend to use the device
What format your media is in.
If you are starting from scratch (i.e.: you don't own a lot of MKV files, or have downloaded a lot of torrent files), then Apple TV is a one-size-fits-all appliance. I use it for my iTunes and iPhoto content, and am very satisfied with the results.
I had a large DVD library and none of it had been digitized, so it was simple to encode it for the Apple TV. Now, I have all (or almost all, anyway) of my music, photos, and DVDs instantly accessible.
If you want to surf the net, have general-purpose solutions (being able to play all formatted files) then a Mac Mini is your answer. While it isn't an appliance like the Apple TV is, it is a robust solution, complete with a DVD drive.
So, my question to you is, how easy do you want it?