I think a "purist" would let the player do the decoding in "Source Direct" mode and then set the receiver to "Direct" mode.
The reason is because the "Direct" mode has the best measured specs.
I have a Denon DVD-3800BDCI & the AVR-5308CI. Both pretty much have the same audio & video circuitry. So if I were going the "purist" route, I would let the 3800BDCI do all the decoding in Source Direct mode and set the 5308CI to Direct mode.
However, I let the receiver do all the decoding because I just get this huge GRIN on my face from seeing that LCD screen read "Dolby TrueHD" and DTS-HD MASTR".


In terms of sound quality, I doubt there is an actual significant sound difference.