Prepreg results in a wider range of dielectric constant on the board, because the prepreg supplier is only specifying the raw material, not controlling the assembly process. So when it is assembled, the thickness of prepreg will be changed and it is not so easy for pcb houses to control the product thickness. This means that controlled impedance layers should ideally be core material.

Generally speaking, core is more reproducible than Prepreg, for both thickness and dielctric constant. It is made in a factory making core to a specific thickness.For using core, it is better for pcb fab to control the thickness of the whole product.

It answered all my puzzles.Very helpful.