The lott will recoil more then a rigby fo sho. FYI, numbers wise basing on 10lb rigs at expected velocities for each: the 458 lott with 500gr bullet puts out inexcess of 70lbs of free recoil. The 416 Rigby with 400gr pills is 58lbs. Compare that to a 375 H&H with a 300gr pill produces around 37lbs. My 338wm with 250gr pills isn't much off the H&H, memory serves me correctly it was 35.5lbs. 225gr are about 34lbs. These are just numbers they give you an idea what report to expect with different cartridges, but in no way the whole story. Everybody reacts differently to felt recoil.
The 375 H&H has to be one of the most used cartridges for DG. Part of the reason being for its ability/performance but remarkably shootable (to more people). It is more affordable as you have found out & has a more practical side to it, as well.