Based on stats from the Databook, Asuma would win...but stats aren't that good a means to decide things like this. Umm....Asuma has done more impressive things that I can recall, but Yamato has done interesting things as well.
Statwise, Asuma has better taijutsu, strength, and speed, which fits with what we've seen, and no disadvantages, but to counter that Yamato has his Kekkei Genkai which is an advantage over normal ninjutsu.
Wood strikes me as more flexible, but the air trench knives seem sharp enough to cut through even them pretty easy.
The speed difference isn't so severe though and it boils down to a ninjutsu user to more of taijutsu fighter.
I'd go as far to say that none of his wood techniques would help him. I just took a look at all of the ones from the manga and none of them seemed like something dangerous for Asuma.
Though I think I may tip my hat to Yamato anyway. His earth techniques seem large scale enough and he can hide on the walls. And I believe his water techniques might assist a lot with his offensive games, where he can use wood for clones and such.
Would be a close fight though. And it could go either way depending on where they're fighting.