Well I can tell you that the 3808 is an excellent unit.....I have been nothing but thrilled with mine. I was looking at the 876 as well when considering my upgrade but decided to go with the Denon for a number of reasons. Both are excellent units and it will really come down to your needs and usage habits. Seeing as how you are not going to be using the Reon processing, as you stated the AVR will be mostly for Blu-ray and 360--that is the real edge that the Onkyo has in terms of video processing.
Also the Onkyos run very hot and cannot be in a closed space, so if you have a AV cabinet it won't be good idea or you will have to install fans. All of that aside, I choose the Denon in terms of sound, connectivity, and reliability. Not to mention that the new GUI on the Denon is absolutely fantastic. Several people around here on Audioholics have gotten the 3808 for $1099---a price you should be able to get matched or come very close to...