I've played quite a bit with .357 and .44 mag shot shells. Best results - by far - have been .44 and cases formed from modified .303 Brit. shells cut to near cylinder length and blown out for the extra shot volume.
With my best .44 loads and #9 shot I wouldn't attempt rats or snakes further away than about 10 feet. Anything further away than that the pattern gets too thin. Even with my enlarged .44 "shotshell" cases, there just aren't enough pellets to shoot any further with any confidence.
Even with Speer's shot caps I'd cut that 10 feet in half with the much smaller shot volume .357.