Issues to keep in mind with each:
Denon AVR-3310CIs (as well as 4310/4810 and reportedly 3311s) have chronic network card failures. If the networking features of the AVR are important to you, the Denon is a bit of a risky proposition. Denon claimed that the problem was restricted to early production runs on the xx10 units, but the appearance of the same problem on the 3311 would lead me to doubt that.
Onkyo receivers are notorious for running very hot. I have no personal experience with the NR808, but it's a common thing with Onkyo's. If you have very good ventilation in your installation, not a big issue (and you get the bonus of cutting down on your natural gas bill

) but when I did have an Onkyo AVR, the heat issue did concern me. The other thing to be wary of with Onkyo is the video processing. The NR808 utilized Faroujda video scaling which is very poor as compared to the ABT used by Denon. If you intend to run your cable or satellite PVR through your receiver, the Onkyo will do a poor job of processing video. The ABT processing used by the Denon 3310 is vastly superior.
In the price range you're looking at you could also look at a Pioneer VSX-1125-K or Pioneer Elite VSX-32. Both these units feature Marvell video scaling with excellent implementation by Pioneer. The Pioneer units will outperform the Denon in this regard.
The other unit to consider is the new Yamaha RXA-1000, although it doesn't use a video scaler in the league of the 3310 or the Pioneer units. Step up to the RX-A2000 and the HQV Vida upscaling should be very good, possibly better than the Denon, but not in the league of the Marvell QDEO used by Pioneer. That said, it's a price jump from where you're looking.
In other words, if networking features are important to you, be leery of the Denon. If video scaling is important, the Onkyo just cannot compete and be aware of the heat issues with Onkyo AVRs.