in the end depends on the tube amp and the tubes used on the tube amp itself. The Elise is a "warmer" OTL tube amp so it makes the HD800 more natural sounding imo while it makes it lose some of its accuracy. "More" Bass oompf for instance. It's hard to describe how distortion works for me. The RME ADI-2 is also a fantastic pairing with the HD800 for that matter but I'd always advice people to try out amps if they can.

In theory all amps should only amplify the sound and do nothing else but tube amps are different in that regard as they will add distortion, if you like the distortion or not is something highly subjective in the end and a swapping out tubes is another rabbithole altogether...Some people like tubes and some don't (and that's completely fine)