Do you think the writers of the Constitution believed one was the branch of government more important?

I don't believe so. I believe they wanted the branches to be evenly important. Balance of power, you know.

https://www.google.com/search?q=three+branches+of+government&oq=three+branches+of+government&aqs=chrome..69i57.8541j0j7&sourceid=chrome&ie=UTF-8