The 605 only has 2 x HDMI inputs and only 1.3a, but does 7.1. That leaves you a bit limited. The 820 'should' have 4 x HDMI inputs, does 1.4a, but only 5.1. If I were to select, I'd go with the 4 x 1.4a HDMIs with 5.1 rather than be limited to 2 x 1.3a HDMIs. As darcilicious
stated, pop everything HDMI through your receiver on input and have a single HDMI cable from receiver to TV.
The 7.1 is nice, but I guess I'm not tuned in enough to hear the difference between it and 5.1. Once you tune up your speakers based on where you comfortably sit, I doubt you would too. I'd go with the Pioneer and keep everything going to and out of the receiver.--
That's "MISTER" Kafir to you.