Whiteshark has it right.
All in all I don't think you did anything too wrong, but his advice is sound. For the last couple of years I was bouncing part time (I am 6'0'' and 185) at a local bar where there can be alooot of fights, and when I worked I was the only bouncer.
One of the things that really does seem to help defuse a situation, is as he said, ask questions if you can, if you had time. In your situation it almost sounds like he was just charging at you and if you opened your mouth to speak he would have just thrown a punch, but for future reference. Whenever someone wanted to start a fight with me or someone else I would pull them aside with my hand on their shoulder so I could clinch them into a guillotine if need be (...aaaand I'm suddenly distracted because a woman just ran into my ER with a boobies out...) and ask them "What do you do for work?" They would say "whaaat?" And I pull them aside again aggressively, and ask what they do for a job? Then remind them why they are stupid to fight ,because the cops will come and they will go to jail and lose their job, etc.
Another thing, well the primary thing I think is just always act super duper cool. Because people are like mirrors, and will reflect your attitude, like a child. As they get angry, you stay ultra calm, and they won't know what to do, and will suddenly become confused and calm down too.
That's just kind of always been my technique for dealing with uptight assholes and it works. A couple of months ago I was hanging out at a downtown bar and stepped outside to give a girl directions on the phone. While I was on the phone, three guys ran up to me, one of em got in my face with his fists all balled up like he was gonna swing on me right then. He was yelling "Is this the guy?!!" and his boys were backing him up. I'd never seen him before.
I didn't hang up the phone, or acknowledge him at all, I just looked at him straight on and stepped a little closer to him, talking on the phone, droning out his words, ready to take a punch if I really had to then headbutt him or kick him right in the kneecap. Just kept talking on the phone, cool as a cucumber, other hand in my jacket, looking right at him. All the sudden he changed his mind, and his boys came up to kind of pull him back, and he went to shake my hand and apologize saying maybe I was the wrong guy. I just pointed down the block and mouthed "Go."
Anyways, sorry for going off on the story. But I think you did pretty good except for the "Next time I see you..."
Being as both of you were probably Martial artist/MMA/boxer's of some kind I guess both of you just started off like you were in the ring instead of the street. I'm sure you would have acted differently if you didn't think it was a boxer and some dude that really wanted to kill you instead of just punch you though.