[Yo-Yo]

... the recoil is vastly different,...

Why? its still a buffered system. Do you feel any significant difference between a lower velocity .223 at say 2400 ft/s and an M193 5.56 round at 3200 ft/s? I can tell but it doesnt affect how I shoot.

F=MV². Recoil goes up with the square of the velocity change, assuming both projectiles have the same weight.

I have no first hand experience, but from what I've read the .277 Fury brass and .277 Fury Hybrid case have a very noticeable difference in felt recoil.

[Magnum44]

I have decades of shooting these platforms. Yes, like I stated, I can tell the difference. But its not enough to matter in terms of changing how you shoot. Your F=Ma (not F=MV^2) is not accounting for the buffer assembly absorbing a large portion of the recoil in the AR platform.

[NorthMountain]

F=MV²

F = ma = d/dt(mv)

KE = (1/2)mV²

I think what you're trying to say is:
m1v1 + m2v2 = m1V1 + m2V2

Given that m1 and m2 (bullet and rifle) are both at rest before firing (ie: v1=0 and v2=0) then

m1V1 = -m2V2

Which is to say that after firing, the momentum of the gun and of the bullet are equal in magnitude but opposite in direction.

Therefore, in general recoil varies linearly (not geometrically) with bullet mass and bullet velocity. It is left as an exercise to the reader that for a given cartridge and load, heavier guns will have a smaller V2 and consequently less felt recoil.