Much voodoo is involved if you really want to get into it. Generally, yes.Much voodoo mentioned here. Short answer,
All other things equal, a round in same brass, same bullet, same primer: the load with the least amount of powder required to achieve the target velocity will have the least recoil.
to crystallize this: in a 470 nitro express, using RL15 instead of H4831 results in same regulation velocity with more than ten pounds less recoil!
Much like accurate medium distance shooting: you can get a million power scope and have a laptop sitting there to crunch data from weather stations every 50 yds or have an experienced shooter ballpark it and go.
A couple of other areas I have found that greatly impact perceived recoil are bullet weight and stock fit.
With respect to bullet weight I find some of my high velocity smaller calibers (300 Win) have more perceived recoil than some of the DG rifles even after factoring in rifle weight into the recoil equations. To me the high velocity cartrages, even though they have less caclulated recoil. are a slap at your face and a a jab at you shoulder compared to the hard push of a DG cartridge such as the 470NE. I have found this effect is magnified by the effect of the high mounting required of some of the current scopes. The high scope mounting requires a loose check weld allowing the rifle to establish an upward velocity and forcefully impact the cheek due to dynamic overshoot. On the 300Win I had signficatly less perceived recoid when I changed from a higher mounted Swaro Z6i scope to a lower mounted Zeiss Victory HT scope even though the rifle weight is less with the Zeiss.
The above is a good lead into stock fit. A well fitted stock allow distribution of recoil without "hot spots". I have two Heym 450NE doubles that are essentially the same weight. The first one is an off the shelf 88B and the second is an 89B that was stocked to fit me. Given there are some other factors, such a where the weight is concentrated on the two rifles; but the different stock shape and fit between the two rifles makes the 89B much more pleasant to shoot. I also found the perceived recoil on the 88B was reduced signficant when I put a pad on the back of the triggger guard. The more closed grip on the 88B caused the second finger to be bashed no matter how the rifle was held and was quite painfull and just a few shots would bruise the finger. The more open grip on the 89B does not have this problem.
Yes. quick n dirty is lighter bullet = higher velocity = less time in the barrel = shorter off-on-off of the force like whiplash vs push.