I don't see any difference between the two.
1) John was the one to drive the getaway car.
2) John was the man to drive the getaway car.
Can't these sentences mean two things:
a) John was the person who actually drove the getaway car. John was the one who drove the car.
b) John was the person who had been assigned the task of driving the car. We don't know if he did drive it or not. Maybe the whole plan fell apart and he didn't drive it or....
I think '1' is ambiguous, but '2' only means 'b'.
I don't think that the second is incapable of carrying both meanings, but I think that the second is more likely with it. I also think that the second would be a better way of expressing that he was the best qualified person to do it.