.357 Magnum = 125 gr. @1400 fps or 158 gr. @1200 fps (approximately, IIRC)
.30 USC = 110 gr. @1900 fps
I would think the sectional density of a .308" 110 grainer would equal or surpass a .357" 125 grainer (don't have any manuals ready at hand . . .).
Using good expanding projectiles, I'd rate the .30 USC as at least the equal of the .357 magnum, fully up to the task of a typical SC whitetail (100 pounds, plus or minus) at ranges inside 100 yards.
Where'd you pull THAT pathetic .357 load from?
I load a 180 XTP/JHP to 1401 fps out of a 6.5" barrel
I also load a 158 grain cast SWC to 1470 fps out of the same gun.
These loads are available from the factory from Buffalo Bore, though the 180 BB uses a cast bullet.
Your load looks more like .38 special +P and I'd NEVER EVER think about hunting deer with a 125 grain JHP, not enough penetration. Good self defense bullet, not so good for game. Stick to 158 and up.
Out of my 20" Rossi carbine, I push that 158 grain load to near 1900 fps. IIRC, the 110 grain Carbine load is around 2000 fps? Just checking the Speer No. 11 manual, they list a top load at 1960 fps. The .357 out of a rifle length barrel is considerably more stomp and can push a heavier bullet in a larger diameter. The .357 with a nice wide, flat nose doesn't need to expand to kill deer quite dead. None of mine went more than 20 yards after being lung shot.
Buffalo Bore lists their 180 at over 1800 fps from a 20" barrel. I can't get that with my handload, using AA#9, perhaps something slower like H110 would be better out of the rifle barrel, don't know. But, that load is so accurate out of my Ruger revolver, I've stuck with it and I don't hunt much with the .357 carbine. I have better rifles in bigger calibers. But, it's a neat gun and capable out to 100 yards on deer sized game.