Man in the Moon
I actually don't know what to write here, because I don't seem to actually understand how MiM functions, but I'll try to write something, or at least my feelings at the relationship between these two.
Even if we start with the fact that Bunnymund is older than MiM, first thing that comes to my mind when thinking of this relationship is that both of them respect each other and the fact is that Man in the Moon is the leader of the Guardians, as the fact that he was the first guardian, when Bunny was still hidden in his warren making chocolate and obsessing over eggs. But the fact is that MiM saw the goodness in Bunny and knew he was able to be the Guardian and the fact that Bunny is the guardian of life and hope, without Bunny there is no Earth, the planet that MiM loves so much and wants to protect the children of it.
So in my opinion these two are two creatures that respect each other, and this
leads to wanting to help each other, aside one being the leader of the Guardian
group and the one who chooses the Guardians.