Definition of medium bore, somewhere between .240 and .350, I think most of us would agree that big bore starts with .400. With the magnums, short magnums and ultra short magnums, this question is not as easy to answer. However my favorite is
7mm-08, light recoil, inherently accurate and can be made from .308 brass if necessary. I have 3 and they will take care of anything in Texas where I live. I have 7, .308 winchesters in several configurations, bolt action, and semi's, not necessarily for hunting. 3 long range rifles, 2 M1a's, and 2 scout rifles. I have been shooting the 7mm-08, since it was introduced in 1978, and it has always been pleasant and delivered in all 3 of my rifles, which by the way are all 18' barrels.