It seemed rather apparent to me that Onkyo decided it was more cost effective to reserve the better amplifier for the higher model. The 805 and 875 had the same amplifier section. You will see now that the 876 still weighs 50 pounds, and you noted the 806 slimmed down from it's older brother. The 805 was certainly better in terms of power, but the 875 had a huge price difference to it with only a few gains (video processing being the most notable). The 876 offers the same video processing as the 875, but the 806 still has just the Faroudja DCDi (only this time it upscales)
The 876 puts out a ton of heat, that's due to it's very inefficient (but very effective) Class A/B design. The Onkyo uses 4 output devices per channel, and has a mamoth power supply. It can deliver monster amounts of power.
The SC-05 doesn't have the video scaling prowess of the Onkyo but also has an awesome amp section. Using the ICEpower Class D topology it's a far more efficient design. It's going to run cooler in high level output situations, while the Onkyo runs hot as hell when it's not doing anything. Considering it weighs about 40 pounds and is THX Ultra II cert, I would venture to say it's got every bit of power that the Onkyo has, possibly more. The Pioneer is also prettier to look at sitting on your AV rack with the high grade glossy finish and amber lighting (it's just a sexy machine).
FTR: the SC-09 measured extremely well (very close to spec'd rating)
http://ultimateavmag.com/avreceivers/908pio09tx/index7.html