Difficult question, Buzz--because I don't necessarily regard the 2nd barrel as only a 2nd shot option. If I'm hunting pheasants or prairie grouse (especially later in the season), I may want a pretty tight 2nd barrel because I'm going to get longer shots--in which case I'll go to my back trigger on a longer range flush, immediately. (I know . . . some will counter that doing so leaves you with a very open first barrel for a followup shot. But I'm willing to live with what's essentially a single barrel in those cases, if I think most of my initial chances will be pretty close--which I do, in good bird country and with good dogs.)
If you're talking something like woodcock and and ruffed grouse, the latter especially earlier in the season when the woodcock are still around and there are quite a few leaves, I don't think you need much more in your 2nd barrel than you do in your first. And it's very seldom the case that your initial look at a ruff will be long range, unlike open country birds. I can count on the fingers of one hand the number of times I've gone to my tighter barrel for the first shot at a grouse. Pheasants, on the other hand . . . I remember a hunt a few years back where I went to the tight barrel first on 3 birds in a row.