Byron, you're absolutely correct. As an example when I was doing the pattern testing on my Benelli I had six (6) choke tubes and six (6) loads. My chokes were Cylinder, Improved Cylinder, Modified, Improved Modified, Full, and the Kick's Gobblin Thunder extended ported at .660". The loads were from Remington, Winchester, and Federal in 2 3/4" Magnum and 3" Magnum .12 gauge number Four Buckshot.
In my gun the Federal 3" load out patterned all others. I had been using the same Winchester load you mentioned above in my Remington 870 with a modified barrel with good results. However, the Federal load was consistently the best throughout my test in all the chokes through this gun.
With that said, all the chokes didn't pattern the same. Modified was poor, Improved Modified was really quite good, then the factory Full blew the pattern and made it look about like the Improved Cylinder. The Kick's tube brought everything together and was head and shoulders above all the rest and actually shocked me how well it would shoot. I shot until I found the right combination. I did the same for my Dad's Mossberg 500. His also shoots the Federal Premium 3" the best and he uses a Hastings .660". It won't quite pattern as well as my set-up, but Dad knocks em' down with his.
I looked out the window this evening and there were two coyotes mousing in the field across the road from me. An adult and a pup. I couldn't take it. I grabbed the Benelli and called the pup across the field and into my barnlot where I smoked him at about 35 yards. Bang - FLOP! I love living in the country!!!