PTSki,
Welcome to the forum...As for your intital question both of the AVRs you started off with in your original post are both very capable AVRs. I use a 3808ci with my RTi12's and it does the job just fine. As strube alluded to, the video processing in the 876 is going to be superior, but you did not specify that as a needed feature so I have no idea whether or not you will even benefit from that.
As also mentioned, the Denons probably have a better reputation in terms of the reliability, but that is debatable. However, on the other side of the coin, the power supply in the 876 is probably going to be more robust than what is found even in the 3808ci. Personally, I would go with the 3808ci over the 876. The Onkyos run hot, so if you have closed space you will need to be careful with that in mind---the Reon plus the amp section equals a very warm AVR. Now if you can find a good price on the NR905/906, then I might lean more towards that unit...