Same wgt gun. 243 with 80gr bullets will have noticeably less recoil than 6.5 with 120-140gr bullets. (E=MC squared). Approx. 7ft# vs 12ft#
Does it matter if they're launched at different speeds?
yes , for a very direct comparison my 5.56 AR and my 300 blackout AR have nearly identical components the barrel is different and the gas tube is shorter on the 300 blackout same buffer , same BCG
the 5.56 launches launches a .224" 55gr projectile at 3200fps and the 300bo a .308" 110gr projectile at 2168fps
the 300 actiually has less felt recoil , not just because it is moving 1000fps slower , the 300bo burns all the powder int he the 16 inch barrel , the 5.56 does not
much of recoil is the expanding gasses pushing back on the muzzle
burn up all the powder in the barrel and you have only the push of the bullet and not the rapidly expanding gasses
use a blowgun on an air compressor air pushing on air does have a recoil effect , same at the car wash water pushing on air has a recoil effect
this is why if you have extra gas at the muzzle the brake works so well to reduce recoil it redirects it up and back significantly reducing the pressure pushing back on the muzzle from the front
if I ran the same bullet in the same gun at the same speed but used a powder that burned before the 1/2 way point in the barrel vs one that was not done burning when it exited the barrel , you would also see a recoil difference. we would have to use a fast and a very slow powder and accept lower velocity than possible but we could see the difference.
we want max accurate velocity to get greater range so we generally have powder being burned right to the muzzle causing a pressure wave of expanding gasses in some cases a fire ball if shot in the dark.
if recoil was just a function of velocity X mass
110 X 2168 =238,480
55 X 3200 = 176,000
the 5.56 should have only 73% of the recoil of the 300bo but the 300 actually has less felt recoil from the same everything else , why it is using a powder that burns in <16 inches
think about engines what gives a greater push a high octane fuel that gives a push over longer time component or a very low octane fuel that explodes and has a very short time componenet engine the same more octane = longer power stroke = more energy to the crank shaft
with a short pulse of power the rifle can't move till it overcomes the inertia of the rifle , with a longer push the inertia is overcome then the additional force is added
also why having a properly fitting stock to shoulder fit reduces felt recoil , the gun is stopped from moving before it can start , but a sloppy shoulder fit the gun has time to get moving then hit the shoulder. like placing your fist with your arm bent a little against some one shoulder then pushing like your punching vs punching where you have time to build up velocity velocity kills at both ends.