I do not have any specific data on that. But I can give you my personal data on crossbow hunting success rate.
I hunted with verticals for many years then had to go to a crossbow due to a physical condition. I hunt the same places with my crossbow as I did with my verticals. Shot distances are the same. I still fill all four of my tags every year just like I did with my verticals.
Nothing has changed with my success rate since I went to a crossbow.
The main aspects of my hunting that has changed is I find it more difficult to pack a crossbow, they are heavier and more bulky in general, when compared to a vertical.
I find the two positive aspects of a crossbow are I do not have to draw it when shooting at a critter, and the scope. With a very bad shoulder and bad vision, the crossbow really shines in those departments.