mo:
You're thinking is pretty right on.
IF the guns weigh the same, using a 90 gr. bullet, going 2986 fps in the .25 WSSM and a 90 gr bullet going 2972 fps in the .243, the .25 WSSM needs roughly 2 grains less powder. The difference in recoil is .24 lb of free recoil energy, with the .25 WSSM generating less recoil. Is that enough to make a difference? I doubt it.
But, in this instance, do both guns weigh the same?
I looked up the Model 7 in 7-08 and without a scope it weighs 6.5#, but I'm guessing that it has a scope, which will bring the weight up to around 7.5# - 8#. The Rossi in .243 weighs 6.25# sans scope. So lets say the Model 7 is scoped and the .243 isn't. Using the same 90 grain bullet/load in the Rossi, and a 140 gr/2500 fps load in the 7mm-08 changes the recoil to 10.07 fpe of recoil for the 7mm-08 and 9.35 fpe of recoil for the Rossi in .243. The .25 WSSM shooting a 90 g bullet 2986 fps in an 8# gun = 7.07 fpe of recoil.
That's roughly 30% less recoil for the .25 WSSM providing I'm guessing correctly on the gun weights that he's previously shot, and that the guesses on the bullet weights/velocity are correct as well.
Another thing that affects perceived recoil is noise and muzzle blast. If he's not wearing hearing protection, all bets are off. (earplugs in kids can be inserted incorrectly, and might not offer the same protection that they will offer adults) I prefer to have kids use electronic ear muffs whenever possible. My nephew even wears them while hunting - HIS choice!