I have both and prefer the Mini. You can just do more with it. With BM-Link or Linkplayer and Beoport you can set it up to work with your B&O equipment and be controlled by your B&O remote. With ATV you need a B&O TV I think. I use Plex to play ripped DVDs on my Mini and iTunes from it for the music. I can use Frontrow with the actual iTMS purchased TV shows and whatnot. With the Mini I can keep hooking up as many hard drives as I want. If I'm watching a movie and suddenly want to look at IMDB of info I can do that on the Mini as well.
Back to using Plex and ripped DVDs, I can rip them right on the Mini and add them into Plex all in one shot. Also, everything is locally there, all the music, all the movies... I don't have to get on a computer and stream something over to the ATV.
The only thing I ever use the ATV for anymore is slideshows (I keep all my photos in Aperture on a separate Mac so it's easier than sending them to the Mini) and renting movies from Apple. The Mini is just a far superior device and you can do far more with it. Which makes sense since it's a full blown computer. I have the bluetooth keyboard and mouse for it that I leave somewhere handy if I need them. Usually just the mouse is necessary because you can control everything remotely with the iPhone or Beo4 anyway.
Edit: If you're interested, here's my setup: http://img691.imageshack.us/img691/5971/bosetup.jpg