Off the top of my head, and by no means researched or confirmed to be accurate:
The 3808 has
1) New Graphical User Interface (GUI) replacing the old On Screen Display (OSD)
2) Networkable adding internet streaming, firmware updates, and picture viewing.
3) HDMI 1.3a support
4) Decoding of DD+ DD-HD DTS-HD and DTS-Master Audio
5) 4 HDMI inputs as opposed to 2
6) USB flash drive support for Music Playing
7) Audio Restorer for play back of highly compressed material
8) 8 position Audyssey as opposed to 6
9) support for optional I-Pod dock
I'm sure there are other features, but these immediately come to mind.
As for which you should get, only you can decide. Both are very capable units.