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: 

- Don't own a TV and therefore own no AppleTV.

+ Control BeoPort via MacMini+LinkPlayer.  

The MacMini sits in my studio but is hardly ever touched; it sleeps most of the time but is awakened and starts playing whenever one hits N.MUSIC or N.RADIO in a MasterLink room.  Control with Beo4 is very extensive but if one feels like searching for and finding very specific music, I just pull an old iPhone which now sits permanently as as if it were an iPod Touch and control the MacMini via Remote.app.

I use both mac mini and apple tv's.

The mac mini is the more powerfull and flexible system and (with the beoport) works well together with B&O.
It's a full fledged computer that (in my case) runs plex and itunes in combination with linkplayer and beoport connected to my main B&O .

Never liked the apple tv's 'itunes locked' system that needs to be hacked to make it somewhat useful. Also mind the dated interface and limited hard drive space. 

I use the 40GB apple TV's solely as secondary (link room?) players  to stream content stored on my NAS to my tv's.

imo the macmini is arguably apple's best value mac

really superb little computer , dual core now and really fly's w/ snow leopard !

Like quite a few of the replies above, I have both a Mac-mini and Apple TV.

I would say the Mac-mini wins everytime. Running LinkPlayer through a DACmagic converter to the BeoPort it's a great source of music on the B&O network and full computer too. I also put all my movies on an external hard drive and then through Wifi stream them form the Mac-mini to the AppleTV. Works beautifully.

Best regards,

Rob