what are the advantages of a centrifugal over a screw and vice versa?
Screw will heat the intake charge more and that is nearly impossible to counteract 100%. Screws will be very efficent over a blower style and even a centrifugal when the screw is modern deainged. But the centrifugal will hit higher boost and make more power.
I suggest you watch videos from Richard Holdner on YT as he has comparison data that shows you the power curves. There is no clear winner it's more what you're trying to achive. But Centrifugals are by far the cheapest to setup as you can keep the stock exhaust.
Again Richard Holdner has testing evidence that proves superchargers work with stock exhaust manifolds.
Once you watch enough of his content you realise that you should pick a good N/A setup that younlike then just add boost.... And like I said rhe cheapest boost is a centrifugal charger.