My first handgun was a 4 inch Ruger Security Six which I wore almost all of the blue off before I traded it away.
My second handgun was a 6 inch S&W 629 both of these I shot extensively as I handloaded for both.
Try a .44 magnum out before you buy one its recoil over prolonged firing strings can be stout to say the least, some people find it objectionable others actually enjoy it
The .357 is a good mid range or mid bore cartridge (.36 caliber to .40) it shoots flat and hits fairly hard and is rated quite well with the right bullet weight in stopping power surveys taken from actual street gunfights over the years.
The .44 is more expensiuve to shoot it kicks allot more so if recoil bothers you one can load it with .44 specials or use reduced power handloads.
If deer and two legged varmits are all you are concerned with the .357 will do what needs to be done.
Out here in the West though I personally prefer my .44 for most things old Elmer Keith had it right big hole in big hole out lots of blood out, easier to track.
Evaluate what YOUR needs are and choose accordingly with the .357 you share calibers and now have two defensive pistols.
The .44 is heavier to carry and is more expensive to buy factory ammunition for and more expensive to reload for as well.
I have had a couple Rugers they are built like tanks the Redhawk is solid design built like a heavy sledge hammer. I only wish mine were as accurate as my Smiths.
In double action revolvers I tend to favor the lighter N frame Smith & Wessons.
Out here in the West I prefer the .44 but thats because I do not want to get charged by an angry moose (again) or take a second or even third shot if hunting animals bigger than deer.
YMMV
Best of luck