I believe you would be happy either reciever. It looks like the Onkyo is a couple hundred dollars cheaper. I own the Denon 3808 and am very pleased with its performance.
I have a HD cablebox with a HDMI out, and a PS3 connected to the reciever, so I can not comment on how well it will upconvert video. I am happy with how it handles the HDMI switching\video pass through.
Currently I have a 5.1 setup, so I haven't been able to test out the Dolby TrueHD or DTS-HD decoding. However, I plan on purchasing two more surrounds in the near future....
The one feature that the Denon 3808 has that the Onkyo TX-SR 875 does not is that it can be networked, and is DLNA certified. This was one of the deciding factors as to why I purchased it. Currently I am using a linksys wireless ethernet gaming adapter to link it to my home network. This allows me to stream FLAC audio files using a media server (TVersity freeware) from my laptop to the reciever.
However, if you have a PS3 you can accomplish the same wireless capabilities since it is DLNA certified also. I own a PS3, but use the denon GUI to play all of my music streaming from my laptop.