These screws previously performed the following functions
Both measures are intended to improve the accuracy of the watch.
Screw balances can be found only in high-grade watch movements. This applies to the past and the present. From today's perspective a screw balance brings no more advantages due to extremely low production tolerances with usual balances. However, some watch movements are still manufactured with screw balances, as they are a feature of high-quality watch movements, and also nice to look at.