Copal #1 = Compur #1 as long as both are cock-and-shoot or both are press. Press shutters have the diaphragm located a little closer to the rear of the rear tube than do cock-and-shoot shutters of the same size (0, 1).

When in good order Copal and Compur shutters are functionally equivalent. I've seen posts to the effect that Copals aren't as long-lived and that Compurs need to be cleaned more often. Can't vouch for either assertion, do have some unrepairable Compurs.

Aperture scales probably won't transfer. And has already been pointed out, a properly cleaned (and lubricated and adjusted) Compur shouldn't give trouble for years after the CLA was done.