I tend to use Improved in my 20 and modified in my 12.
I think your logic is backwards on this. Someone correct me if I'm wrong, but the only difference in 12 ga vs 20 ga is number of pellets, where 12 ga has more pellets. Velocity is the same. So given that, IC for 12 ga and mod for 20, here (theoretically) your pellets density is the same, velocity is the same, but a 12 ga gives you a bigger pattern.