For just math calculations, the listed factors matter. FELT recoil is different, and several other factors ALSO have significance.
The "platform" matters. The .357 Mag and the 9mm Luger are not the same round, despite having the same working pressure in SAAMI specs.
Most of the difference in felt recoil is due to the different guns used to fire the rounds. Semi auto vs DA or SA revolver.
The rest of the difference is the rounds themselves. Generally speaking the .357 Mag uses heavier bullets at higher velocities than the 9mm Luger.
Ask one of the guys who has a Ruger Blackhawk .357/9mm convertible what the difference in recoil is like. Same gun, you just change the cylinder. 9mm recoil is less, or so I've heard.
I have the other gun where an equal comparison can be made. I have a Contender with both a 9mm and a .357 Mag barrel (same length 6"). In that gun, 9mm is DEFINATELY less felt recoil.
Comparing the typical semi auto to DA revolver involves many factors that obscure the actual difference between the two rounds.