Hard to answer that without more information. What is your experience with shooting, and with those particular calibers? What is your experience with deer hunting, and what kind of deer hunting are you doing? cornfields, thick woods, etc?
My personal experience is that when you are hunting with a revolver, it is similar to archery hunting; you want 2 holes for bloodletting. Obviously .45 is bigger than .357 when it comes to hole diameter.
I shot a spikebuck in the shoulder with a .357 Remington Corelokt round, 165 grain jhp (1200 fps). Bullet broke shoulder, but DID NOT penetrate the chest cavity, deer was tracked and killed with shotgun rounds.
I shot two small deer this year with a 255 grain swc, probably about 850 fps. Kicks a lot less than a .357, and penetrates without question. Not a flat shooter, so ya gotta get close.
If you are going to hunt with a .45colt, handloading is almost a necessity.