Since you are wondering about the recoil differences in the two calibers of revolvers let me play the devil's advocate here . . . since I own several .357s and a .44 magnum too. My main deer hunting/hog hunting "rifle" is my Model 29 S&W .44 magnum REVOLVER, with a 6" barrel. Has been for years and years.
My suggestion?
For your first "serious" revolver I'd recommend a fine .22LR revolver! TWO HUGE REASONS:
1. You won't develop the "curse" of learning on a hard-kicking revolver . . . since the "curse" I refer to is the curse of never being accurate with a revolver due to starting with a hard-kicking revolver that "cursed" you into developing a really bad flinch!
The main thing you want to get from your first revolver is proper technique and learning to watch the muzzle flash when it goes off. If you are flinching at all your eyes will be closed!
2. Centerfire ammo is very, very expensive! Get the .22LR revolver and a couple of bricks of 550 rounds per box of .22LR ammo and you will learn to be a great shot and be able to master your technique shooting a couple of thousand rounds of .22LR ammo very cheaply.
2,000 rounds of centerfire magnum ammo will cost you well over $900 . . . money needed for devoted practice that you could have gotten with purchasing 2,000 rounds of .22LR ammo AND a .22LR revolver. It will pay for itself . . . the .22 revolver will thus end up "free!"
Then, when you have mastered that .22 revolver you'll also have enough experiences shooting revolvers to make a great choice between a .357 magnum and a .44 magnum revolver too!
OTHER SUGGESTION . . . Find a good handgun instructor to teach you proper grip, trigger technique and how to master your accuracy! Accuracy is everything with all firearms, but especially important when considering any handgun caliber.
PS: If you insist on going magnum revolver right out of the chute please do two things:
1. Leave a couple of empty cylinders when you load and practice, and before shooting spin the cylinder around a few times so you do NOT know when the gun will go bang or not. Then, you'll see the viscious over-compensation you will be making thinking the gun will be going off when you pull the trigger over an empty chamber! Better yet, have a friend load it for you with varying numbers of full and empty chambers! You'll quickly learn not to flinch!!!
2. Consider the .357 first, and load it for practice with 148gr. lead wadcutter practice ammo in .38 special instead. This is super accurate stuff and it won't be hard on you or the gun.
Then, if you use it for home protection, down-load it to .38 Special for indoor defense. Touching off a .357 magnum round indoors will temporarily both blind you from the muzzle flash and deafen you due to the very loud report! Worse, it overpenetrates and thus might zip through 2-3 interior walls and kill a loved one. Instead, buy some .38 special defensive ammo for home use.
Save the .357 Magnum ammo for times on the road or when you know you don't have the types of walls that can zipped through with a .38 special round!
The .38 Special is a serious self-defense round in its own right, and .38 Special ammo is actually in .357 caliber anyway of course, for the marketing guys over 100 years ago chose to call the new .36 caliber ammo .38 Special instead, since .36 caliber revolvers using black powder were used in the Civil War era and they didn't want to confuse folks into thinking the .38 Special ammo was the same stuff with the same level of performance!
BTW, my magnums in various revolver calibers, and my .45 autos remain in the safe most of the time. My "always" on me CCW handgun is the 5-shot Model 37 S&W revolver . . . in .38 Special . . . and I feel totally well protected! As will all handgun shooting, BULLET PLACEMENT is the key.