I'd say a large determing factor would be what the sound characteristics of your system already tends towards! If your speakers/system combo already tends toward the Analytical side (or empasizes bright tracts a bit), you'd probably do better with the Parasound, which is a bit warmer overall (especially bass), and is a little more forgiving on the top end. Conversely, if your sytem is a bit soft already, then the ATI would do well in that it's a bit more neutral and etched sounding (more high end accurate pressentation...by a tad).
Both amps have plenty of current and drive. They both have excellent build quality. The ATI is a bit more I believe.
However, for an over all home theater first type of amp, the parasound overall get's the nod from me in that is has all the qualities you really should lean towards in a home theater system. It has a stronger bass punch and bass line, is slightly forgiving of the harsher source materials, and is a bit warm (which is a more easily pleasing sound, especially with film tracts). Over all, I think the sheer listenablility with movies/music dubties would tend to make me lean more towards the Parasound.
I once heard this set up at a show using a Parasound 2205. I think it helped produce the single best HT set up sound at the show!...and there you are.