How/why is a driver better at screws than a combi drill?
Impact drivers are much better for screwing.   Period.   You will lose less heads and as a user you will have to put less weight on it compared to a drill.

This is because impact drivers have more rotational torque but they also bump (tap) the screw at around 30 times a second.    The drill might have more rotational power but that is what gives it problems.    This power stresses the user to push towards the screw or the screw head to be well made or you will get a slip or head damage.   

The impact driver will usually stall before it needs to power through to the point of causing damage or slipping.   The tiny taps it commits to allow it an interval to stall on vs. the user hitting a snag with a drill and committing to adding more pressure right before the stall or getting a slip.   

For just screwing things in an impact driver wins bigtime in home construction.   The drill is needed for drilling but often used for screwing because it is a jack of all trades.   Watch any good craftsman do woodwork (kitchen cabinets) and they would never use a drill to secure cabinets together and things like that.