In general, the .44 will have more recoil than the 357. It is using more powder to hurl a heavier bullet. However, there are so many unknowns to compare these two cartridges. Felt recoil vs. perceived recoil due to muzzle blast are two unknowns heavily dependent on the load and barrel length. Felt recoil is also very dependent on grip style and material, as well as how you hold it. Lots of folks have love/hate relationships with DA vs SA grip styles. Similarly, some like rubber grips and some do not. For me, I have a .44 SA Ruger SBH with smooth Lett grips and I find it a pussycat to shoot even with heavy loads. I take a low grip to avoid having the trigger guard smack my knuckle. I used to have a S&W 629 that I put rubber Gripper grips on, and I hated it. The gripper grips were too narrow across the backstrap and really pained the web of my hand. I also have a Ruger SRH 480 that had the Hogue rubber monogrip on. I found the rubber gripped the meat of my hand and could really start to sting after a while with heavy handloads. I switched to a smooth wood Hogue monogrip and I love it. My only complaint now is that the thumb dimple is a bit too high for my stubby fingered hands. My thumb ends up on the bulge instead of above it in the dimple. That tends to whack the side of my thumb joint after a while. My point of all this is that it depends on so many factors such as your grip position, the gun's grip style barrel length, bullet weight, load, etc. Everyone has opinions, but their opinions willl be specific to their combination of these factors.
I agree with the earlier poster that your best bet is to try out guns of your buddies, or go to a range that has rental guns and try some out. Then, you can be a lot more sure of making the right choice for you. Or, you can take the shotgun approach... Buy several different models, try them all out, keep the ones you like, and trade the rest on new ones!!
Good luck
