The curve appears to break more sharply than it actually does, but it doesn't appear to break more than it actually does. Watch a pitcher throwing curves from the side and then watch them from behind the plate. From the side the break is fairly gradual. From behind the plate it appears to be a much sharper break.
The reason the break seems so much sharper is that we can't track the ball well enough from behind the plate so we track the ball at release, estimate where it is going to end up based on what we normally see, a fastball, and then when the ball isn't where we expect it when we pick it up again closer to the plate our brains put a sharp break in between to explain how the ball went from where we expected it to where it really was.
The same phenomena also explains why lefties seem to have such good movement. Our brains expect the ball to tail in to a righty and they include that in the estimate of where the ball is going to be. When it ends up where we expected it to be our brain supplies a straight line. Then a lefty comes up and the ball tails away from a righty and we think the ball has moved twice as much as it really has.
If you doubt this just go back to your earliest little league days. The fastballs from those pitchers were coming in dead straight as far as we could tell. Now go look at a young little leaguer and you'll see the ball looping in there because it is thrown so slowly.