When you're in the same ballpark in terms of power factor and gun weight, then a heavier bullet travelling slower will feel gentler, and a lighter bullet travelling faster will feel snappier. That's why, for instance, folks who reload 9mm to shoot in Production class in USPSA load a 147 grain bullet moving 851 fps, instead of a 115 grain bullet moving 1087. Even though they both just make the required PF of 125, and may be shot out of the same gun, the heavier bullet just feels softer.
But that kind of thing really only comes into play as a secondary factor, if you're shooting a similar PF in a similar platform. It's not nearly a big enough factor to overcome the diff. between a .357 and a .44 mag--unless the mag is shooting real slow loads. I've got a .41 mag load that pushes a 225 gr bullet at 900 fps. That's around the same PF as the 158 gr. .357 going 1250 (a little higher, actually), but it feels like an absolute kitten. Lower report and flash can also play into the perception of the recoil, usually in favor of a big, slow bullet.