No doubt that a 12 gauge is more powerful. Simple Mass times velocity, given the shot size is the same. Most of my 20 gauge loads are 1oz at 1220FPS, my favorite 12 gauge load is 1 1/8 oz at 1400FPS. Obivously the 12 gauge is more powerful.
Now if you tell a dove or quail that he is better off being hit with 5 pellets at 1000fps compared to 4 pellets at 950, I am thinking that he may argue with you if he was not dead!
Both guages are excellent and I highly prefer my light smooth swinging 20 gauge. For big birds or long distance clay shooting, I of course go with the 12 gauge to get the higher velocity and more pellets in the pattern.
As far as choke goes, a full is a full is a full. Gauge does not matter. You of course have more pellets in that pattern with a heavier shot charge though. The smaller gauges also tend to string out the pattern more, which can actually make it easier to hit a crossing target.
Chukar opens tommorow and I will be using my 12 gauge, because I will be using #6 shot and the shots tend to be long and going donwnhill. My wife will be using a 20gauge with hot 1oz loads and the chukar probably wont know the difference. I just feel more confident with a little more shot and velocity.
Good shooting,
Brian