More on this would be more generally used in speaking. For example: The budgets will be cut this quarter, but more on that later. It is a way of declaring your intention to return to that subject at a later point in dialogue. Whereas, moreover means that you are adding input to the subject now, but possibly from a different angle. Moreover would be better applied in academic writing.

I would say that "moreover" is more suited to academic writing. Can you give an example where you think one could use "more on this"?