Yes, the .44 magnum is more powerful (and recoils more) than the .357 magnum.
In a Colt, the gun would be the Anaconda.
For S&W, the Model 29 or 629 are the most common.
For the most common loadings for each:
.357 magnum - 158 gr @ 1200 fps = 544 ft/lbs energy
.44 Magnum - 240 gr @ 1325 fps = 935 ft/lbs energy