Given a pellet of 00 buckshot weighs about 53.8 grains, if one does the math using one of the online muzzle energy calculators, an 8 pellet 00 load @ 1600 FPS delivers about 2440 ft. lbs at the muzzle. A 12 pellet 00 load @ 1325 FPS delivers about 2520 ft. lbs. at the muzzle.
I'm not sure many folks can detect an 80 ft. lb. difference at the shoulder when firing a 12 gauge shotgun. I'm pretty sure I can't.
That being said, I have no doubt that reduced recoil 00 buckshot is extremely lethal at across the room/down the hallway distances. I would not want to be hit with either of the above two loads.
Yeah, I know the math, I love it in fact (I also think that metric calculations are not only easier, but in terms of energy, they make more sense). I majored in it in college, and one thing I learned is that theoretical data is not the same as perceived experience. For that reason, I collected a lot of different types of 12ga. buck, from #4 to 000, reduced recoil, full power, and magnum loads. I haven't tried them all yet as the military range I use won't allow shot --only slugs. But I can say that the Win. XX #4 3" mag with 41 pellets has had more recoil than anything else I've tried, including the Fed. 3" rifled slugs, the Fed. sabot slugs, and the Fed. 00 3" mag.
I know that, mathematically, different burn rates will translate into different recoil (ie, a slow burning powder produces less recoil, but for an extended period). Also, the muzzle energy of a load is a function of distance. For recoil, I would think that impulse, a function of time, would give a better comparison of actual forces at the shoulder. A slower burn rate resulting in longer, weaker recoil would intuitively seem weaker than a faster burn rate resulting in shorter, stronger recoil. I don't know. In earthquakes the opposite is true. But there are much more variables at play here than just distance, time, and rate.
The math can get quite complicated if one were to introduce multiple variables (for instance, your own shoulder, weight, etc.). This would give a better analysis, but by what degree? If enough variables are introduced, one can get multiple solutions, or solutions that don't have satisfactory results (like terms that cannot be resolved) --which, in physics, leads to experiments. If I have to experiment anyway, then I will use the simpler equations, like energy and such (the ones we all use and quote) and stay away from diff. eq. Also, some things cannot be quantified satisfactorily, such as one's own sensitivity (in regards to nerves, pain threshold, etc.). Plus, the experiments are more fun...
I don't know if I can tell the difference between the Fed. 00 12 pellet and the Hornady 8 pellet at the shoulder. I have 'em both, but haven't compared the two yet. Unless the Hornady has a marked reduction in recoil, I would agree that the 12 pellet Fed. would be more desirable. The Hornady has to have that going for it or it won't be worth the price, or worth losing the extra pellets. All the Fed. stuff being equal, if the recoil is similar, I would probably go with the 000. If 8-12 pellets of 00 is enough at various velocities, then 9 pellets of 000 at 1325 will be more than enough.
So, the reduced recoil loads seem to come down to this: high velocity, lower pellet is only worth it if perceived recoil is significantly lower. Nevertheless, higher pellet and lower velocity is not so easily resolved, since here the same pellet number moving slower may still have advantages at close range.