As a manstopper, the .357 magnum has certainly earned its praises, and probably about as effective as a handgun caliber gets. The classic 125 grain jacketed hollowpoint load that flings the bullet at 1400+ fps has had a very good track record. This is something that both the Marshall / Sanow crowd and the Fackler crowd can agree, it seems.
A .44 magnum is certainly more powerful. Just as a comparison, a .44 magnum can launch a 250 grain bullet (twice the weight of the above mentioned .357 magnum) to the same velocities as the above load. If anything, the heavier loads are great for hunting, even up to a black bear. However, for manstopping abilities, there's no advantage.
Keep in mind, though, that full power loads in the .357 magnum, and certainly the .44 magnum, are going to kick a good bit. In these cases, where people might be recoil sensitive, the .357 magnum will have the advantage. For folks that can't even stand that, Remington does make a medium velocity .357 magnum load that duplicates the feel of a hot 9 mm load (125 grain bullet, 1200 fps). Easy recoiling, for certain, compared to a full house .357 magnum.
For those that can't even stand that, they can always fire .38 Special cartridges out of a .357 magnum revolver, or .44 Special cartridges out of a .44 magnum revolver. Both can still be decent manstoppers, especially the .44 Special.