Take it with a grain of salt, but the reason I ask about your skill level is to determine if having that extra capacity will make a difference to you. Pretty sure if you miss with the 2-3/4" shell, you'll miss with the 3.5" shell as well. From what I've heard they are punishing and expensive. I kill ducks & geese with 2-3/4" shells regularly, and only rarely will I bring 3" shells. If I can't hit them beyond 40 yards, I stop shooting. The shells are capable of killing them, it's just a bit beyond my skill range.
The 3-1/2" guns are heavier, have a longer stroke, and are more expensive. For what you are doing - mostly clay targets - a 2-3/4" gun would be perfectly capable. It will also handle ducks very well as long as you keep it under 40 yards.
Something like a Rem. 1100 in either 12 or 20 would be just dandy. With very low recoil on the skeet field. (And there are a couple on the EE right now).