What dictates who should be on Derse and who should be on Prospit?

Not much, honestly. With the Extended Zodiac we have confirmation all Aspects can be both Derse and Prospit, and we have examples of different Dreaming Moons for different Classes. It’s not even by Active and Passive- Since Hussie explicitly mentioned how Derse Dreamers are influenced to be more Active, as seen with Rose, who was supposed to be a Passive Class, and Prospit influences them to be more Passive, which we can see in Jade, who’s supposed to be a Highly Active Class. Hell, we know thanks to Sollux that we don’t even need to have the same number of people in each Moon.

In the end, the ONLY thing that determines something, is Ectobiology. Only the characters that are paired to make their children/parents, and the children/parents themselves seem to follow the norm- The Strilondes to Derse, the Harleybertcrockglishes to Prospit…

Of course in a real Session, there would not be any Ectobiology, since that is reserved to the Session that spawned the Frog Temple- Making the Players to predestine them to play it so the Frog Temple can arrive in the first place. So in reality? Seems another matter of Personality, as seen on the Quiz.