I'm also in the camp that says something like "play well" or "good luck" when starting the match. At the end, if I win, I like the idea of just shaking hands and maybe a head nod, and that's it. If I lose, I wish them luck in their other matches.
As competitors, I think we all know that there is a difference between being beaten, and losing. When someone plays so well that I'm just outmatched, I take that loss and move on. But if I make mistakes and screw up opportunities, and lose, that's different. I don't really want pleasantries if I lose, at least not right after that match.
Had a guy I met playing that is a good guy, and probably a bit better than me. He wins more than I do, and each time I learn something. We played again in a tournament after about a year of not playing, and I felt like I was much improved, so hoping for a better outcome. I made a couple dumb moves and didn't play anywhere near my ability, and he beat me good. He could see I was not happy, and kept trying to make positive comments, which only made it worse. I know him enough to know he was genuinely trying to lift me a bit, but I was too pissed at myself then to hear it. Losing has to bug you a bit or you'll never get better, at least in my mind it works that way. He ended up winning that tournament, and I was happy for him. But I remember how I felt after our match, so I learned not to try to cheer anyone up after a match.