Well, Gingerbread Man doesn't have any magic, but I'm not sure if 401 does either.
If that's true, then I imagine G-Man would ultimately win, because of 401's mental state impairing her decisions.
However, 401's insanity could also make her an unpredictable opponent too (sort of like Captain Jack Sparrow from Pirates of the Caribbean)
So I think that, assuming that 401 doesn't have magic (which she might, I don't know a ton about her), it could somewhat go either way, though I'm just going to say Gingerbread Man because creator bias (:-P)