One of the advantages of fanfold labels is their ability to restack themselves. Roll labels can curl as they print, especially if large batches of labels are being printed at once, and leave large messes of labels spread on the floor.
Fanfold labels do not have this problem.
As the labels print, they fold where they are perforated and restack themselves. This makes for an easier clean up as labels are not scattered around the work area. When using a desktop printer, you will simply need to make sure your printer is elevated for fanfold labels to stack properly.