In Flaves particular case, not sure we can quantify what the difference would be. However in the long run there would be one. You may not have seen a difference, but when the big boys and girls play for keeps, they don’t use LW 28gauges. There is a difference, and if there wasn’t, they would be shooting the 28 for recoil. Nor would it be a LW one.
Addition: if you would ask most of the top guns why they use 1 1/8 ounce, the answer would be because the rules say they can’t use 1 1/2.
You are most likely correct and for full disclosure, I tend to use heavier guns for sporting also. I am not good enough nor seriously enough to consistently shoot in the 90s, but have shot with a few who do, and from memory, they all were shooting 12 ga sporting guns with 1 1/8 charges of shot, so you are probably correct. I personally shoot better with 1oz 2 3/4 dram in my 30" Beretta 391 Sporting in that the reduced recoil helps me over the course of a round or two and I do about the same with my not super light 30" Beretta O/U two barrel set Sporting gun ( 682 I think, but can't remember), though only when the 28 ga barrels are installed. In my experience, a little additional weight if balanced well helps me as does a little longer barrel and lower recoil loads do, too.