Given there are a lot of different games that you can shoot and some need two barrels, you may need to find a different set of chokes. The only time I will make huge size changes is when I shoot Skeet.
For Skeet I will shoot a Skeet (SK) and a Improved Cylinder (IC). SK in the bottom and IC in the top. Since you can select to shoot top or bottom barrel first I think it works. For the fly away birds I will shoot the IC then the coming at me birds I shoot the SK. This gets tricky when you get to into it and forget to switch the barrels, but then again the difference in the choke size is .005 of an inch.
For almost everything else I like to shoot a Modified (M) and a Full (F) or the Extra Full (XF) on top. This is where I think it turns into a real mind game.
In trap I will shoot a M on the bottom and a XF on top. Given you only get one shot at the bird, but if you hit a bad streak and gotta pick it up it seems to give you a much better focus and timing if I switch to the top barrel and shoot the XF. Then switch back over to the M. I have tried shooting anything from LM to XF on trap and find that M is the most consistent with me. This is the same setup I will use if I shoot Int'l Trap. Easier to carry over then to switch them out.
When shooting Sporting Clays the birds come at a bunch of different angles, I may open it up to a Light Mod(LM) on the bottom and a M-XF on top dependent on how the birds are looking.
Doubles Trap you know EXACTLY where the birds are going to be going so I open it up to a LM and F. See flash of orange and fire away and you killed it then pick up the second one and pick it off. Very easy.
Keep in mind that your personal shooting style and choke tube selection go hand in hand. But this is not to say a good shooter can't shoot a SK on trap and still break a 25. The important thing is to not get to frustrated to quickly and switch out chokes and change everything. If you consistently are missing birds then your baseline or pre shot routine may be the problem, especially if you aren't keeping your head on the gun!
Here is my shotgun with only a XF Briley Splash Choke:
Here is my shotgun with two Briley Extended Chokes in it:



