you mean for corners and freekicks right? because in open play for the past few decades everyone marks zonally, sometimes with the exception of putting a specific player in charge of defending oppositions playmaker / best player 1v1. if they didn't defend with zonal marking, the fullbacks would never dare attacking.
for freekicks and corner kicks I'd say in the end both depend on the quality of the players, I haven't seen sufficient data to suggest that man marking or zonal marking leads to less dangerous situations from corner kicks, if zonal was absolute disaster every time, it should be evident in the data. for sure man marking is easier to implement though, zonal needs a lot of prep. some of the stigma towards zonal marking set pieces probably comes from where the blame is placed when you concede - for zonal the system is usually the culprit while for man marking the individual usually is the donkey.