I'd go for a 7600GT AGP and add a quiet aftermarket cooler if it were my HTPC. Of the cards you meantioned, the X800XTpe is just as fast as the 7600GT, maybe even beat it a little more often than it loses. It doesn't have Sm3.0 though which if priced the same would be the tiebreaker in favor of the 7600GT in my eyes. Not to mention, the 7600GT consumes less power...better for your 350W PSU (check the 12v rail of the power supply to see how many amps it is). The power supply is definatelty a factor here as it may not be enough for the higher end cards.
I own a X800XTpe and am very happy with it. I also have a AIW X800XT, and You may also want to consider that one as they are useually cheaper, slightly lower clocked/slightly slower, but have a TV tuner and remote control, as well as the VIVO breakout boxes. And I have used many X800 pro's. The X800 pro is a step down from either XT or XTPE, but still a very decent card if priced significantly better than the others. Forget the 8-pipe X800GT though.
The 7600GS is definately weaker in games than the X800 pro. Same features as the 7600GT, but much lower clock speeds...therefor slower game performance. The 6800GS is faster and still has SM3.0, but in AGP, the 6800GS's are lower clocked and honestly at stock speeds a X800 pro would beat it in most titles. But priced the same it's still a good option if you really want Sm3.0.
One other thought, my HTPC is in an Antec Overature case. It's a mobile Athlon XP and a 9800 pro with a VGA Silencer on it. I went for quiet and run the fans low speeds. But without increasing some air flow, I'd have a heat issue with a card like the AIW X800XT in that system. Something to consider depending on your case design/size/airflow.