There is a rule but it's not very simple.

You can calculate the power required by the propeller. For a given speed it increases directly with the pitch but goes up by the 4th power of the diameter. So generally a small change in diameter makes a lot more difference than a small change in pitch. Of course it then gets confusing because the larger prop runs slower and that reduces the power required to some extent.

I bet that was a lot more than you wanted to know .

Steve