1) In redgards to boxing, as an above poster has mentioned. I believe the dominate angle of attack seperates alot of pro's and ammys. Alot of amateurs I have trained with, move simply 2 dimensional. In and out, side to side. Cutting at a 45 degree angle is more of a professional way of thinking, but more simle, reacting. The instinct to move around the punch, and not just to move around it, but strike while doing so or as soon as your slight movement stops. Versus the ammy guys who like to back up on a large wild swing, or side step on a powerful straight. Versus that cut in, they just don't seem to have that reaction time which is my second point.
2) The reaction times. Alot of pros seem to respond to things, again as mentioned above, much swifter. To see an avalance of strikes comming your way, remaning calm, and relaxing, taking appropriate action, acknowledging the destination of a strike, appropriatly moving around said strike, and attacking with appropriate reach, and strike/combinations. Alot of ammys get overwhelmed, and this emotional state dramatically cuts down anyone's reaction time, professional or not. Its remaning calm that allows time to be calm and still, and pro's have this within thier being, not just knowledge. Many don't even know they do it, it just becomes habit and apart of thier character, to not react, but respond.
3) From a Mixed Martial Artist standpoint, I would suggest a huge learning curve, as most MMA's are much more well rounded today, the fact of knowing simplicity in complexity. The skill of the pro's today make everything look easy, in which most cases it is, such as going from a leg kick, imediatly moving around a 2 or three punch combo as a 'scared' or 'startled' response, into the a take down, maybe failing on the take down and jumping right back up avoiding being pulled down and immediatly back to kicking and on the offense. The transition of one aspect of the fight to the next like its second nature. My point being, alot of ammy guys think too much, and dont just let it be. The thought process of, 'ok were standing' 'ok now I am in a clinch' 'ok he just tried to take me down, are we standing? yes/no' 'oh im on the ground'. These, however in most cases very short, miliseconds if even that, its the aknowledgement of the transition, versus the allowance of a transition to just be. I guess that re inforces reaction times, however this is just based of my own personal experience, in which was a learning curve I once had to overcome myself. All three points my be very uniquely different in your view, but from my experience, three noticable things I have picked up on, not even just ammy to pro, but even the TOP pro's, vs entry level pro's. Happy training fellas.