I work at a shop where we sell the Yamaha and Denon AVRs you asked about, so I have first hand experience with those, but not the HK. I would have to say that both the 1020 and 2313 are well built, musical sounding units. You get a lot for the money with the Yamaha Aventage series for sure. What I don't like about how Yamaha designs their units is the severe taper they give to the volume control. I.e., a person has to crank the heck out of it to get any volume at all, coming close to 0dbs, as they label it. I will say, any bass frequency shortcomings can be equalized for with the Yamaha.
For the casual user though, I prefer the audio EQ presets on the Denon, and ultimately even more on units like Onkyo's 616, 717, or their Integra divisions' DTR series . Onkyo and Integra use more straightforward naming conventions for the presets, and they include THX Cinema modes, which actually work quite well when the system is not being fully calibrated. Test drive an Onkyo TX-NR717 if you can.
If I had to suggest one based on those you originally asked about, I would prob say the Denon. It will save you a few bucks over the Aventage too.
As usual, best thing you can do is get to a locally owned shop and test out the units you are interested in.