I provided some examples of how the recoil of different military rifle cartridges compares in Assault Rifle: the Development of the Modern Military Rifle and its Ammunition. I worked out nominal "recoil energy factors", if the cartridges were all fired in guns of identical weight and design. The figures run like this:
5.45x39: 24
5.56x45 M855: 32
7.62x39: 59
7.62x51 NATO: 142.
The .30-06 develops pretty much the same recoil as the 7.62x51 - in other words, about four times the recoil energy of the 5.56mm, with the 7.62x39 AK round being about half-way in between.
Which model Browning? Which make and model 12 gauge? What type of ammo are you using in each?I find a 30.06 (browning semiauto) and 12GA to have similar recoil.
It all starts with Newton's old "equal and opposite reaction" law of motion. The bullet is propelled out of the barrel at high velocity. Recoil is simply the 'equal and opposite reaction' to the motion of the bullet. Of course, the rifle is much more massive than the bullet, so it needs to move much more slowly in the opposite direction in order to 'equal' the motion of the bullet. It is also possible to 'dissipate' some of that 'opposite reaction' energy using a 'recoil pad' (the energy goes into deforming the pad, which then of course 'springs' back but this creates a 'delay' which spreads out the recoil).