Personally, I don't think there is a difference between 1 1/8 oz vs 1 oz shells for registered targets ...either in Trap, Sporting Clays or Skeet..../ yes there are more pellets in a 1 1/8 oz load...but the 1 oz shell, in my experience patterns better - with less flyers out of the pattern.
Whenever I shoot registered ....I shoot 1 oz loads in a 12ga ...and 90% of the time its 1 oz of 8's at about 1225 fps..../ but I carry a few boxes of 9's - for a really close target or a battue - and once in a while a box or so of 7 1/2's for rabbits, or long range targets...( but all 1 oz at 1225 fps )...
But confidence plays a role in all these games - and if anyone thinks that a 1 1/8 oz shell gives them an edge / then that's what they should shoot. But that 1 oz shell that I shoot - gives me about 15-20% less recoil than a 1 1/8 oz shell...and over a 3 or 4 day tournament, mental fatigue plays a role, and I'm more on my game - with a little bit less recoil.
But for shooting with your buddies ....I'm dropping my 12ga loads to 7/8 oz ..and I'm starting to load some 3/4 oz loads vs shooting my 28ga ...and in the heavier 12ga gun / its an even softer shell in the 12ga.