Sorry about the buil-up and then lousy conclusion. I was tired.
I think we'd all agree that the fight would last a number of rounds. So then we would need to know the levels/hit dice any impartial DM would assign to the two. I'd say the hit dice were equal, as 1 hit point doesn't justify an extra hit die.
Demogorgon's energy draining would quickly bring Asmodeus down to a level where Asmodeus would not get a save vs. Demogorgon's hypnosis ability.
I see demons as more powerful than devil individually, but demons fight each other and don't cooperate. Charge! is their general idea of strategy. I think devils, although individually weaker, ccoperate, plan, know tactics and strategy, and don't really fight one another outside of politicing and plotting. That's why devils win as much as lose.
I'm still using 1e as a basis, because I am one of those who try to forget 2e, as well as the movies Sphere and Highlander 2.
BTW, I'm a fan of both. I prefer neither. In fact, in one campaign I ran, Asmodeus and Demogorgon had arranged a "partnership" of sorts.
As for demons, Demogorgon - Orcus - Juiblex were, and always will be, the best, with honourable mention to Lolth.