If you go to the different manufacturer's websites- somewhere burried in all the info they provide will be the heights for their rings. Yes, there can be substantial difference from one "medium" to the next. Burris rings post "medium" heights as being about .27" whereas Warne lists .375". Both those measurements should be from the very bottom of the ring assemblyto the bottom of the scope. Leupold seems to have hidden their specs.
Another considerationis the positioning of the scope. Certainly you will want to have the scope mounted such that you come up naturally to a full field of view and with max eye-relief, but sometimes a scope will offer a bit of fore and aft adjustment and still yield a proper fit. The position of the eyepiece and adjustment ring can make a huge difference inwhether you areable to easily operate the hammer.