Most "professional" manual lathes have both rack and leadscrew features fitted. Some very small lathes may dispense with the rack, and their leadscrews are permanently coupled to the saddle - a handwheel on the end of the leadscrew moves the carriage. Once we get to CNC machines, all bets are off.
A handwheel on the apron drives the lathe saddle through some gearing which ends in the pinion that engages with the rack. This provides for "quick and dirty" movements of the saddle along the bed, irrespective of whether the lathe spindle is rotating or not. I have also seen some lathes with very heavy tailstocks equipped with a system for racking the tailstock roughly into position before using the tailstock quill for more finely controlled movement. On some very large machines, the rack movements may even be motorised.
The leadscrew is usually coupled to a set of gears (often in a gearbox mounted in front of the headstock) that allows the leadscrew to rotate in a fixed ratio to the rotation of the lathe spindle - the ratio being set by the gear train selected. The apron usually carries a "split nut" mechanism which allows the lathe saddle to be coupled (or un-coupled) with the leadscrew as required. This is how we are able to cut threads and also provides for saddle fine feeds. Professional machines often save wear on the leadscrew by providing a separate saddle drive system.
So the short answer is: rack for quick and dirty movements, leadscrew for slower movements in direct ratio with spindle rotation.
Don't underestimate the potential of the handwheel-operated rack feed system. I have been able to produce balls of adequate quality when the quantities and time available did not warrant making a dedicated ball-turning attachment, by roughing out with combined cross- and rack feed and finishing with a file followed with an emery polish.
I hope this helps you.