A load of equal weight and equal velocity will impart the same amount of force, regardless of whether it is a 12 or 2012 gauge shells are typically more powerful.
Oneounce, my friend, I'm not sure where you're going with this. Let's see if we're of like minds, we aren't in some areas. I gotta agree with, "12 gauge shells are typically more powerful" if it means 12-ga loads typically deliver more shot than 20-ga loads. However, I suspect you're thinking that two identical loads: say a 12-ga 1-oz load, at 1200-fps has the same muzzle energy as a 20-ga 1-oz load, at 1200-fps. This is also true.
But, from our experience, we know shooting a 20-ga 1-oz packs more recoil than a 12-ga shooting the same 1-oz load. Why? The obvious answer is the 20-ga gun is typically lighter than a 12-ga gun. That explains some of it. But, I shoot tubed guns, and the weights are the same, but the 20-ga still has more recoil than the 12-ga equivalent load, in the same gun. I suspect it's due to the higher pressure in the 20-ga barrel.
To deliver a load of equal weight and velocity: If F is the force required to get the load up to speed, and F = P x A, as A (area, controlled by the bore) decreases, then P (pressure) must increase. A typical 12-ga has a bore cross section of 1.14 sq.in. and a 20-ga 0.97 sq.in. So, the 20-ga pressure has to be around 18% higher than the 12-ga to shoot an equivalent load. If you want to take the example to an extreme, consider the pressure (and recoil) if you tried to shoot a 1-oz bullet at 1,200-fps from a .30 caliber rifle -- Yikes!
Some of you are thinking, "No way, Zippy's crazy, I've shot 20 and 12-ga guns and the 20-ga doesn't recoil more." Well, you've probably shot standard loads: A typical typical 12-ga 1 1/8-oz has about 29% more shot muzzle energy than a 7/8-oz 20-ga load. This greatly eclipses the recoil difference due to different internal pressures. Try a 12 and a 20 with equivalent loads and your thinking may be changed.
The same applies to other bores. If your are thinking of shooting extra heavy 12-ga loads, you might want to think of getting a 10-ga with an equivalent load; but, the area and pressure differences aren't as significant as with the 20 and 12-ga.