Which is better, and what is the difference?
What is the best time to call back?
When is the best time to call back?
Either, but I'm more concerned about callback. I can see no reason for making it one word.
Either will be understood, but "What is the best time to call back?" is more commonly used.
At a technical level, using "what" is modeling the answer as a generalized conceptual entity, while using "when" is specifically modeling it as a chronological time. Nobody is ever thinking about this distinction when using either phrase, however.