Explain difference please 20v12 gauge

I have read discussions on this topic but do not understand fully. What is the difference between a 24gr (7/8oz) no 8 shot cartridge in 12 and 20 gauge fired through 1/4 choke (improved cylinder)? They both have c390 shot and should put 77% of the shot in a 36” circle at 30 yards. How is one better than the other?

Generally the 20 bores are lighter, other than that there's no real world difference in performance 

My Thoughts on the matter .

A) If you are a pheasant , there is no difference you are just as dead .  
B ) if you are shooting clays for fun and not bothered about a score  , there is no difference. 
C )  I can’t ever recall any report of any big completion or event like the commonwealth or Olympic Games where the competitor used a 20 . Again only my assumption, but that means that the particular benefit of a 20 gauge is in the gun not the cartridge  , basically  it’s weight to carry . This  is a disadvantage in competition  shooting where a heavier /steadier platform is the norm . 

D) from a practical point of view in terms of competition loads , the choice of 20g loads is poor compared to 12 gauge  . 
 

I just base these comments on my personal use of my own 12 and 20 gauge guns 

Same difference. There may be a negligible difference in the 20G shot starting as a 'taller' but 'less wide' cylinder, but by the time the shot is at the target, it will have spread beyond measure.

Being less prevalent, the 20G cartridges will likely cost more. Also the 20G gun, being lighter, will absorb less recoil. Funnily enough I've had discussions with shooters saying they like the 'lesser recoil' of the 20G, but I can't wrap my head around that. Might as well ask, as maybe I'm missing something. 

With 24 grams of shot being expelled at the same velocity, the forces pushing 'back' will be the same in each, but the heavier gun won't move as much as the lighter gun, right? Something about the laws of physics. Now I'm no scientist by any means, but I suspect the shooters who feel the 20G recoils less than their 12G, probably have a better "fit" with their 20G than they do with their 12G. Or am I overlooking other things? 

There’s some evidence to suggest 20g loads produce more consistent patterns at close ranges although that’s open to debate. Aside from that, it’s down to the weight of the gun and perceived recoil. 

I can only think of one occasion when a major event has been won with a 20g and that was the 2003 English Open skeet. Mind you, the chap that won it could have used a peashooter and still been victorious.