I am no expert in the field, but I have an opinion formed from following the sport for a long time.
1) It's important who is fighting, not just what martial art they studied. What shape a fighter is in and what his skills level is.
2) OK, let's assume we are talking identical twins with identical fitness level. Some martial arts are more 'applied' than others. Generally it is accepted that it takes less time to be ready for a street fight if you study Muay Thai or boxing as opposed to Karate or Kung Fu.
3) Going beyond the first two points - this is where the fun starts. It is generally accepted that a fighter with a style for close contact will beat a fighter who fights from the distance. A Muay Thai fighter will beat a Kung Fu, Karate or Taekwondo fighter. So will a boxer, assuming he has some knowledge of how to protect against kicks. And a wrestler will beat a boxer or a Muay Thai fighter. This is what MMA has shown us.
4) I also read that a Taekwondo fighter will beat a wrestler. An animal analogy is that a bird (kicker) beats a snake (wrestler), a snake beats a cat (boxer), a cat beats a bird. I have no idea how a kicker is supposed to beat a wrestler, so just sharing the idea.
5) I also read once that Kung Fu has anti grappling moves which would lead to injuries and are not allowed in competition. No clue what they are.
6) I had a lot of fun when I read about a karate student sparring with boxers and having a shock of his life finding out that karate has no block for a short hook in close quarters