My observations are based on experience with a limited selection of materials: Tri-X in Diafine and stand processed in Rodinal; FP4+ in Diafine.
Under full moonlight I see fairly normal tonal characteristics (assuming I get the exposure right, which isn't easy). In fact, some of my Tri-X exposures when souped in Diafine could almost pass for daylight photos.
Shadow detail can be quite good, midtones can be very normal and highlights tend to be blocked up only where absolutely unavoidable, such as moonlight reflected on the water.
No idea how these films might behave with more typical developers and more "normal" development - haven't tried.
And I wouldn't be at all surprised if objective testing totally refuted my casual observations. I judge my negatives solely by how they print and nothing else. If they "look" like nighttime photos while retaining the tonal characteristics, shadow and highlight detail I want, I'm happy.