Do teams that press handle the press better than teams that don't press?

I don't know the answer. It is possible that, since you know what you do when you press, you are better able to react when other people press you. Possible, but it does not automatically follow. Sometimes pressing teams may be no better than non-pressing teams at breaking the press. Houdini said it was easy to break out of a safe, because safes were not built to keep people "in." Pressing schemes are built to attack the ball, not to break presses. Someone ought to do a study on this.