I only shoot skeet for fun, and practice for waterfowl, so take this as my novice skeet shooters advice and what's been passed down to me by more experienced shooters.
It depends on shooting skeet or wings.
Wingshooting, I rarely bring the O/U for waterfowl, but when I do, I'll shoot 2 of the same, depending on expected ranges, say IC/IC, and I'll shoot bottom barrel first just as a habit.
For Skeet, some folks like to shoot IC/Skeet or Skeet/Open, with the bottom barrel and more constricted choke shot first. Reason being, on the doubles, it's nice to have that top barrel with a more open pattern as, at least for me, that 2nd shot is right on top of me by the time I get to it.
I think it's all personal preference vs an exact science. Plenty of folks shoot the same chokes in both barrels and do very well with it, as mentioned above.