The biggest difference in my opinion, is that the Denon offers Audyssey and a better GUI.
I know that the Yamaha and Pioneer offer their own brand of room correction and calibration, but I don't think it's on the same level as Audyssey, and I think they have really come through with a good version now that you can measure 8 different seats.
Additionally, I can tell you I use the GUI on the 3808 all the time. It is so nice to have the volume come up on the screen when you want to adjust it. Additionally, once you get the hang of it, making small tweaks on the fly is so easy with the GUI. It however, does take some significant time to get used to.