A double-lung shot, no large bones hit (maybe a rib or two), a single shot fired, no shoulder/leg broken? If it was feeding quietly when hit, and not previously alerted/adrenalized, maybe 50-200 yards. If running, already freaked-out/scared by previous shots, then 1/2 mile is not out of the question. A friend smacked a large mid-western whitetail with a .223 softpoint through the lungs, no bones hit, 2" exit wound, but the deer wasn't hit until shot number three, and by then he was already in high gear. Ran 1/2 to 3/4 of a mile, laid down, he shot again and missed (bad move; should have let it bleed out), it got up and ran another mile before expiring (all distances measured, as the deer's path paralleled a road).
Lots of variables in this situation; I wouldn't bet anything at all on any result being certain or near-certain.
As far as your weapon choices, the natural winner would be the big-bore, but with two requirements; you shoot it as well or better than the .357, and it can be brought to zero with the hunting load. I believe "holding off" (high/low/left/right) on game is a bad idea; if you can't zero the gun precisely, then accuracy (and confidence) suffers. If you shoot the .357 significantly better, then use it; the .45 is only a better choice if the bullet hits where you want it to.