Hm...this may depend on who strikes first.
Clearly the powerhouse on Beta Flight is Witchfire (she seems completely unfair by the way, Mungi

). Persuasion appears to be pretty damn powerful as well.
But I still think that the first striker can win this. Karma could possibly take over either Witchfire or Persuasion first before the they can do anything. Then Moonstar (Psyche) can create an illusion to distract the one not taken over by Karma, making the other one believe something else is happening. With that distraction, the one being deceived could be taken out quickly, either by Cannonball or Sunspot, both of which move at sub-sonic to sonic speeds.
Wolfsbane is pretty much useless here, unless she's fighting Goblyn, I guess.
I'm basically trying to think of any way that the New Mutants can win this. And I think it's plausible that they could, depending on who strikes first.
If Beta Flight strikes first, they pretty much kick the NM's asses. Mainly due to Witchfire.