.40 cal. pistol, 135gr projectile, 6.0gr charge, 1180f/s.
Snap. Oww!
Same pistol, 180gr projectile, 5.5gr charge, 940f/s.
Shove. Ahh!
Yes. If the 135 at 1180 generated more momentum than the 180 at 940, it will produce more recoil momentum, and more felt recoil.
No argument there.
With an autopistol, there is a factor that is largely ignored. I noted it once, but I'll repeat it.
The recoil impulse isn't transmitted to your hand in the same way that a revolver does it because it's on a sliding rail. If the slide were mounted on a 30-foot frame rail, without a recoil spring between them...you could fire the gun and feel nothing beyond a mild push from the rail to rail friction. You get almost nothing from the internal ballistic event...or the "explosion" of the powder charge and the resulting action/reaction between bullet and breechblock. What you feel comes from the recoil spring and the slide impacting the frame. Of the two, the slide's impact generates the more
obvious.
The recoil system is a closed system...separate and apart from the main system of the bullet, barrel, and slide. The compressing spring generates a force vector between the slide and frame. As it compresses, it pushes on both with equal force. The faster it compresses, the harder it pushes.
That "Equal and Opposite" thing works backward, too.
The impact with the frame is the one that tells the tale. If the bullet is driven hard enough and fast enough to generate more momentum than the heavier bullet...the slide will have more momentum. The slide will move faster...compressing the spring faster...and it will carry that momentum to the impact point with the frame.
Increasing the spring rate won't change anything. It will slow the slide, but will generate more forward and rearward force as it compresses than the lighter spring...so it equals out. It softens the blow at impact, but is pushing harder before that impact occurs, and you're back to square one. So, it doesn't "soften" recoil so much as it changes the amount of time that the gun recoils...and thus your perception of it. Momentum is momentum and must be conserved. All a spring rate change does is to alter the amount of time that it takes to deliver the momentum to your hand. Go and fire a Browning autoloading shotgun with its long recoil operation...and then fire a pump shotgun of the same weight. The momentum is the same. The recoil impulse is the same. Only the way that the recoil is delivered to your shoulder changes.
So, felt recoil comes from momentum...not the bullet's kinetic energy. We've used the .220 Swift/.45-70 analogy to demonstrate that. You can step it up a notch and fire an 8-pound .308 rifle with a 150-grain bullet at 2800 fps back to back with an 8-pound Sharps carbine with a 405-grain bullet at 1350 fps to demonstrate it. The .308 generates some 2600 foot-pounds of kinetic energy, and clearly beats the big, slow slug...but the .308 rifle isn't at all unpleasant...while the Sharps is decidedly so after about 8 or 10 rounds.
Anyone who is within driving distance can come and try my Sharps. BYO .308 rifle. All mine weigh less than the Sharps...but they still don't kick as hard.