Assuming you are talking about a .44 mag. (you don't say), I believe, as others have stated, the 240 gr. hard cast SWC is plenty gun for (almost) anything.
I loaded and shot many thousands of rounds in my Redhawk. I am not very big but handled the recoil without a problem up to max loads and 245 gr. bullets.
But, the 300 gr. with max-max loads (tested for safety) were more recoil than I care to experience.
Plus, the recoil brought the point of impact up so high my sights would not crank down far enough to get any kind of accuracy with the 300 grainers. Only use I can think of is when Brownie is so close you can smell him and you don't want to be his lunch.