There is of course no comparsion to the increased effectiveness of the smallbore shotgun as there is in the smallbore rifle.
The rifle fires a single projectile while the shotgun fire a Charge of shot. The increased balistic co-efficient of a heavier smaller dia bullet retains its velocity & energy to a much longer range than does a fat short one. Compare a 200 grain bullet for instance fired from both a .30 cal & a .44 cal at the same velocity. The .30 cal one will far outrange the .44 one.
The small round shot having a very low Ballistic co-rfficient do not gain much at all in being speeded up much beyond their normal velocities. In fact the more they are speeded up, the quicker they lose velocity. As the speed of sound is passed drag increases all out of proportion to the increase in velocity.
Unless a great improvement in pattern can be shown for the small bore little is going to be gained, & this is "Highly Unlikely" to occur.
For 3/4oz of shot I would personally prefer nothing smaller than a 28ga, for 1oz othing smaller than a 20ga & a 16 would be even better & for 1Ľoz A 12ga has it all over a 3" 20ga.