I haven't found any secondary info to back this up yet, but according to a dealer (yeah, this could be completely bogus and unfounded entirely) the RX-V663 and RX-V863 use different amplifier types. He says the RX-V863's amplifier will "sound better" and will have "more clipping headroom". I mentioned to the dealer that the use the same power supply with the same volt amp rating, he says that's not entirely correct. He mentioned that the RX-V663 uses a mosfet configuration and the RX-V863 uses some type of amplifier that is more efficient (I can't remember the term he used unfortunately).
I know I have been running around telling everyone that they used the same amplifier, also that it was the same amplifier in the RX-V659 that everyone loved so much. This may all be untrue, but I feel I owe it to those that read and trust my posts to make sure I have not misled you. I made some very quick assumptions (optimistic ones) and I apologize for any inconvenience this may have caused.
I will continue to research this as time and resources permit.
Thank you,
Seth