lovesomeshootin,
I have owned both .257's and 6.5x55's for many years, and hunted a wide variety of both varmints and big game with them. In fact I still own rifles in both chamberings, and love them both.
Both will work great for your purposes, and you would never be able to see a dime's worth of difference between them either on deer or varmints.
In fact with today's bullets I doubt you'd ever see a difference in performance on game bigger than deer. This is based on some experience in observing elk hunters here in Montana. A .257 or 6.5x55 will take elk quite neatly with the right bullet in the right place; if it doesn't the shot placement was lousy, not the choice of cartridge.
