I would produce the state license that matches my residence, first, as reflected on my DL.
Why, just seems to me that is the primary permit and the NH would be secondary although you are in that state.
Another question would be: How well do you understand the NH carry law?
My reason for presentataion of the primary permit is that the officer is most likely going to ask for it anyway when he determines your Non-Resident NH permit is based on another permit. Save him the hassle of having to ask.