Considering that a 12ga might fire a 385gr projectile at 1800+ fps, while a 44mag carbine might do a 240gr at 1800, the 12ga would have more than 50% more recoil.
JMR
Firing a 240 gr bullet @ 1800 fps from a 7.5 lb 44 mag only gives around 12 ft lbs. Problem is most 44 mag carbines are going to be much lighter than a shotgun. From a 5-6 lb gun the 44 mag is going to have around 15 ft lbs of recoil. About the same as a standard weight 308.