Yes, that was the point I was trying to make in a much more long-winded way. Yes, there is a law of physics that deals with conservation of energy, namely the first law of thermodynamics, but if we are talking about physical laws describing the relative motions of objects that collide, or in this case two objects that are affected by an "explosion" between them, it is the law of conservation of momentum that applies.
I know the OP asked about cartridges with different mass projectiles and the same "powder" load, but I am not sure if the intent of the query was to ask what happened with exactly the same type of powder and charge weight in the same cartridge case.
I had assumed that the intent of the question was to determine what the difference was in recoil was with very similar types of ammunition, say standard pressure (P) FMJ loads in the same caliber made by the same manufacturer. Because commercial ammunition with different projectiles is not loaded with the same exact powder charge and type, nor is it loaded to achieve the same power factor across all different projectile masses. Commercial ammunition is loaded to achieve a desired maximum case pressure per SAAMI standards.
If you look at 115, 124, and 147 grain 9mm loads from a variety of different manufacturers, you will invariably see that the advertised muzzle velocity increases as projectile mass decreases. This is true for calibers other than 9 mm Luger as well. But while projectile momentum often increases with increasing projectile mass, it does not do so invariably.
For example, if you look at American Eagle 9mm FMJ ammunition, the advertised muzzle velocities for 115 grain, 124 grain, and 147 grain respectively are 1180 fps, 1150 fps, and 1000 fps respectively. The computed projectile momenta are 19.4 ft-b, 20.4 ft-lb, and 21.0 ft-lb, so in this case momentum does increase slightly with increasing projectile mass.
But if you look at CCI Speer Lawman FMJ, the muzzle velocities for 115 grain, 124 grain, and 147 grain are 1200 fps, 1090 fps, and 985 fps and the calculated momenta are 19.7 ft-lb, 19.3 ft-lb, and 20.7 ft-lb. In this case, the momentum for the 115 grain load is greater than that of the 124 grain.
And to look at another caliber, for American Eagle .40 S&W FMJ, the muzzle velocities for 155 grain, 165 grain, and 180 grain are 1160 fps, 1130 fps, and 1000 fps. In this case the momenta are 25.7 ft-lb, 26.6 ft-lb, and 25.7 ft-lb. The intermediate projectile mass has the greatest momentum.
As has been demonstrated, recoil measured by movement of the pistol in a Ransom rest is determined by projectile momentum, or power factor, which is basically the same thing. But I do suspect that projectile dwell time within the barrel has an effect on the acceleration of the slide in recoil, which has an effect on perceived recoil.