As I understand it, both sentences are grammatically correct, but the second version is used more often. Why? Is that because the second version is less formal? Or are there any other reasons in practice?
Is it necessary to prepare anything else for our meeting?
Is there anything else to prepare for our meeting?
"Is it necessary to" is not a commonly used phrase. It could be used, but would carry an emphasis suggesting "Is it really necessary? is it required?"
If you need to include an idea of "necessity," you can add it to the second example: "Is there anything else we need to prepare for our meeting?"