I'd back the 357 over the 44 mag rossi all day long, especially in todays era of cartridge component shortages. I feed mine a diet of 158 grain tc cast lead bullets ahead of a pinch of Lovex D036 ignited by a small rifle primer, gets me about 900 fps. If I want magnum power double the dose of powder same primer and the bullets leave the 20" barrel at 1570 fps, if I want more I got 2400 powder that adds another 150 fps or so.
The first loads cost me, here in the uk, about the same as 22LR and on our local military range I can hit the charging grunt target every time at 100 yards with the first load using the lousy buckhorn sights.
FWIW the cost breakdown (in USD) per round is cases free, powder 2.5 cents, primer 3 cents so 5.5 cents per round the lead for the bullets is free. Good 22 lr (Aguila match) is around 12 cents a shot. I use Lee dies and presses. If I use magnum loads the powder costs double and a gas check adds about 2 cents so it's still comparable to 22 lr.
44 mag needs large pistol primers as LR won't fit, they are about 10 cents each over here, powder is at least 2.5 times more (6 cents?) so, for me, only marginally more expensive than 22 lr. I just won't buy LP primers at that price ($90 a 1000 last time I saw any for sale).
I have a new Lee mold for TL 158 swc which I will powder coat so they'll be marginally more expensive but not worth worrying about.