What a great conversation. I owned the PS audio gain cell dac and I didn't think it was that good. I've used the PS audio DL3 which was much better. And I liked the onboard dac of the he PS Audio strata integrated. I really like that integrated app so even though it's not hooked up at the moment I do enjoy listening to it and can't quite part with it.
I've had the CXA81 too. Love the sound of that... However it did not appear to have the juice to drive my floor standers as the sound thinned out considerably when comparing between bookshelf and floor stander.
My favorite to date is the electrocompaniet ec6d which I bought second hand. The integrated DAC on that is super. I don't feel I need to pair it with an external dac.
Seems like once you get above two or 3,000 for integrateds The sound largely becomes a matter of what you like. So it can be tough to say what is actually better. Kind of like arguing about what color is better.
hope this helps.