I am definitely no expert so please take my comments as such. I have upgraded from a Denon 3802 to an Onkyo 905, and in my opinion the 905 blows the socks off my 3802 in almost every department. There is allot more power, the bass is far more substantial and better controlled, detail is improved and film surround effects are far more realistic. One thing that really stood out to me was the clarity and detail in the vocals, which seemed to have a move cinematic feel. Although after extended listening and comparing it to the Denon I'm not 100% sure if the treble is an improvement, although I don't think that it is any worst. But please note that I've only had it for a couple of weeks and I think that I need to re-calibrate as the audessey didn't work that well for me.
As for the difference in sound quality between the 875 and the 905, I cannot comment as I have never heard the 875. If you do a search on the forum, it has been discussed before.
I'm very happy with the upgrade and would certainly recommend it, the difference in sound quality is instantly noticeable. Besides if you buy it from the Richer Sounds website (where both 905 and 875 are discounted well) then there is a 7 day cool off period so you don't really have anything to lose ;O)
EDIT: Please note that my experience so far is with standard DVD.