Yes, the .44 is more powerful, but
especially with a handgun, most shooters should not attempt a shot on game at any range beyond 50-60 yards, regardless of caliber. That, I think, is also an argument against scoping handguns. That scope might encourage you to take shots that you shouldn't be taking.
First shot in the vitals. Form field positions. Every time. Nothing else will do.
At the ranges that 90% of us have any business taking a shot at a deer, I don't consider a properly-loaded .357 "marginal."
Is the .44 "better?" Yes.
Is the .357 enough? Yes.
If you're a shooter who can go beyond 60 yards with a handgun, then by all means go for the .44. Also, you have my admiration, because I can't do it. Past 100 yards? Very, very few can go there, no matter what they're got in their hands.
--Shannon
--Shannon