There are three advantages to a rear mounted parting off tool.
1) The mount, and usually the tool, can be pretty much permanently fitted so it’s worth making the effort to get the tool exactly aligned. By its very nature a parting tool is weak from side to side and the cut heavy. The chip also has to come out of a narrow slot so it’s prone to jam. Anything less than perfect alignment makes it harder to get a reliable, clean cut.
2) A rear mounted tool goes direct on the cross slide. Taking the sliding joint of the top slide out of the equation makes things seriously stiffer.
3) The feed screw is in tension pulling the tool into cut. Inherently far stiffer than pushing where the screw can bend or shift slightly in an attempt to run away from the load. The tool can also be drawn into the cut so so things are floating in the backlash region so the tool isn’t properly under control.
It may or may not be instructive to note that capstan lathes invariably have a rear mounted parting off tool. At production quantities you need reliable parting off.
Clive