Fortunately for you, I have both the Mac Mini and the Apple TV. So my take will be based on actual use, not mere hypotheticals based on specs. But like most everything, much depends on personal context.
You made a very valid question: Apple TV or Mac Mini as a media center?
I'll give you two sets of answers: the geek version and the layman's version.
The geek take
The Apple TV and Mac Mini are essentially the same. If you hacked the Apple TV, you'd essentially get a Mac Mini for cheap! Scour the Net for the hacks. But time is money, so that's the trade-off. 15 years ago, when I had lots of time, little money, and lots of hacker chutzpah, I would've taken this route.
The layman's take
But now, I have no time, rusty hack abilities, and still no money.
I certainly considered using my Mac Mini as a media center. But do you really want a bluetooth keyboard and mouse in your home theater? Because you'll likely need one for the Mac Mini.
If you use a Mac Mini as your media center, you cannot play rented iTunes HD movies on it--not yet, anyway. iTunes HD rentals can only be rented and played on the Apple TV.
To recap the
pros and cons of using Mac Mini as a media center:
Pros
* More flexible than Apple TV;
Cons
* Best used with keyboard and mouse, which could clutter an otherwise clean and elegant home theater;
* Cannot play rented iTunes HD movies yet
That said, you may want to consider what I do:
* Use Apple TV as my media center;
* Sync one Mac to the Apple TV, so that media I purchase, rent, or import on the Mac gets replicated on the Apple TV;
* Stream other Macs (two others in my household), so that media on other Macs can play (but not stored) on the Apple TV, via wireless streaming;
* Use iSquint on any of my Macs to convert avi/divx movies onto a format that iTunes and Apple TV can play; yes, it's an extra step, but I do it in batches while I'm asleep or doing other things. (I haven't tried converting an HD avi/divx movie yet)
Bottomline
I like the utter simplicity of the Apple TV. I have probably watched more movies on it in the one month that I have owned it than on my DVD player all of last year. (In fairness, I have an Archos 704 Wifi where I watch most SD movies/shows while I travel, or on my spinning bike.) Still, to rent and watch HD with 5.1 DTS sound without leaving the comforts of one's house--and without having to tussle seeders for Torrent treasures--is an experience every hardworking person deserves.
Like I said, time is money. My Apple TV has already paid for itself in spades.
Hope this helps!