Flat tappet: The wider foot allows for a higher rate of acceleration to be designed into the cam lobe.
Roller tappet: The larger OD allows for using a wheel with a larger radius that translates into a small increase in lifter acceleration.

Those are the potential advantages; whether the flat-tappet cam lobe or roller lifter are designed for them is something different.

Also, a brief PSA that faster is not always or necessarily better.