I owned the DC-1 and have auditioned the AVP, though not extensively. They're both a bit dated at this point, but the DC-1 more so than the AVP. The DC-1 was/is really great on HT - it was a bit step up from my original Denon AVR-3600 for both movies and music, but was a very nice centerpiece for HT. If you can find one that has the 4.0 software and the new remote, you'll definitely have a nice unit on your hands.
The AVP will almost undoubtedly sound better for two-channel music than the DC-1, especially because of the analog bypass mode.
I think Abstract7 made the most pertinent point - how long are you planning on having this unit? If the answer is indefinitely, I'd try to buy the AVP, but for less than $2K more than the DC-1, which I think is possible - it's a little newer, probably will work better for the 40% music you cite, and it's a much sturdier-built piece of gear (minus the remote, which is pretty wimpy). If you're pretty sure you'll be replacing either in the medium term, I'd save the $$ and enjoy the DC-1 as a step up, because it is a very enjoyable piece.
If you're open to two other options, I'd offer up these. First, if you're thinking of spending $3000-3500, you can find a Lexicon MC-1 for that price (used), and I'd take it over either of the units you describe (full disclosure: I did take it over those two units). It is at least tied with the best in terms of HT performance, and sounds pretty darn good for music as well, especially if you like the multi-channel synthesized sound - I don't, but a lot of reviewers like it a lot and comment on Lexicon's excellent implementation. It's a breeze to use, and extremely flexible, so it's both easy and allows for tweaking. Lexicon has a history of very generous upgrade allowances, so if/when they come out with a new model, you'll have a good path to follow.
Second alternative would be to buy the DC-1 for HT, and buy something like a Krell KRC-3 as an analog pre-amp. This setup could be had for no more than $3K, and the Krell has a feature called theater pass-through which allows for easy integration between the two environments, both operationally as well as from a wiring standpoint. This would give you an excellent analog path for music, and excellent HT performance, as well as flexibility for upgrading in the future. -Kirk