"What fear? Of you? No one's been afraid of you since the Dark Ages!" - Bunnymund to Pitch
They are enemies, they go back even before there was life on Earth. The fact is that Pitch is responsible for the Pooka genocide. So, aside the fact that Bunnymund really wants to protect the children, he also has strong feelings about the fact that it's Pitch's fault that he is the last of his spices.
The interactions show that they make each other nervous, and if it was by their plan, the other wouldn't exist, but they still do.
Pitch almost manages to defeat Bunny, when he destroys Easter, and Bunnymund
loses his power because children are stopping to believe in him, transforming
in a small rabbit. In that moment Boogeyman tries to actually mock him, and
scare him, but despite being in the small body he is, Bunnymund doesn't step
back and keeps his vow of protecting the children.