I have a 7PRC and 7mm Backcountry. Honestly feel the PRC has a twinge more recoil. The 7PRC is a 24 inch barrel and weighs 10.3 lbs with scope, the 7mm Backcountry weighs 8.4 lbs with scope and has a 20 inch barrel. Just for context. I shoot both Suppressed with same Aero Lahar 30L can.I haven't shot a 7bc, so I'll start with that, but recoil is powder mass, bullet mass and velocity. Load data for 7bc is in the 55-60 grain range. 5-10-ish grains different from 7rm, depending on powder. So if the bullet weights are the same, and the 7bc has more velocity, it's going to be really close in recoil, in theory.
I'd be curious if people with first hand experience would agree.