As someone who has spent over a decade in martial arts, taking at minimum of two styles at time and for no less than 3 years per style, I can tell you the deaf guy would have the advantage EXCEPT in Judo. If this is Karate, then being able to see trumps being able to hear hands down. I know it's cool to think that you can sense your opponent or somehow hearing them will make you able to dodge their attacks or something... and in some cases, if they are moving slowly enough you might even be able to (for instance, drunk guy at a bar or something. Slow, exaggerated movement, unsteady, etc)- but Karate is FAST. I mean very VERY fast. In Judo you start already holding each other, and you generally do not let go. This means eyesight really isn't important at all. It's helpful for being able to see their footwork, but you really don't have to see to do what you need to do. Feeling their weight, the way it shifts, etc. In fact, hearing isn't important either. Helen Keller herself could have been a pro judo champion!
But with Karate? The deaf guy hands down. I know it's not very imaginative to say that, but reality just isn't as cool as fiction sometimes. 🙁
Of all the posts, this is my favorite. I loled. =D