Recoil comparison for a 7PRC and 7BC at the same speed, with my best estimates of powder charge and accounting for higher muzzle exit pressure/powder velocity increase due to higher chamber pressure (e rif is the column for recoil energy):
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Tiny difference in recoil. We could debate on muzzle exit pressure/powder velocity increase at bullet exit, or better yet maybe someone could run some Quickload/GRT iterations and post those pressure curves for assessment. But from this I don't see a benefit other than maybe the 7PRC cannot actually hit 3k in 20". Running a 28 Nos which I think can do that no problem:
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So in that case there is a more noticeable difference. However I'm now a little skeptical the 7BC can even hit 3k in 20" at 80ksi... again need some Quickload investigations to see if that actually works.
Fundamentally though I don't see the benefit of higher mv with the 175 class 7mm - it's still an 8mph gun and terminal ranges are still STUPID far. It's just more recoil.