The only things that give Vixen an edge are
She is a human with the animal characteristics, which equals BB's actual turning into animals with pros and cons for each one
The healing factor
Force Field which I am sure beast boy can rhino horn away .
And somehow get powers of other heroes that apparently according to the New Earth page, she can do. If she uses other heroes' powers, she would beat BB
And if we are talking about the Arrowverse Vixens, Mari and Amaya,
Mari can turn invisible and has stick fighting skills.
Amaya has swordsmanship and fifth degree black belt karate skills which I am sure outmatch New Earth BB's fighting skills and definitely Prime Earth BB's fighting skills.
Kuasa from the Arrowverse has hydrokinesis which I am sure would give her the victory over BB.
The Titans TV Series version of BB has only been shown turning into a tiger and a snake, but he has mellee regular fighting skills due to training with Dick and Jason, but it is not enough to defeat Vixen.
So I would say any version of Beast Boy other that Titans would beat any version of Vixen other than Arrowverse except if New Earth Vixen is using other powerful characters' powers.
