Well, if you prefer for the turned parts to really be round, like the metal parts of the kits, then turning the tubed blanks between centers eliminates problems with imprecisely machined bushings, mandrels that get warped, flex while turning and otherwise introduce error into your turnings that will ultimately cause your pens to be out of round. Of course, if you don't mind having the centerband proud on one side and shy on the other, mandrels work fine
Actually, It is possible to turn very precisely on a mandrel, but it is much simpler to do so between centers, assuming your lathe tapers are both concentric and properly aligned.
Bushings can make it simpler to turn a barrel to the proper diameter at both ends, but only to the degree that they are themselves concentric and fit the ID of the tubes without allowing them to deviate if the ends of the blanks are not precisely perpendicular to the centerline of the tube. One must also assume that they are the exact same diameter as the corresponding part of every kit you use them to assemble, and that they have not had their diameter altered by sanding or turning over their lifespan. They also tend to cause problems if they are in place while finishing. On the other hand a pair of dial calipers can measure each individual component, and allow you to match the final diameter of the tube to it very exactly, for every kit, and without changing over time.
So it's really just a question of how precise you want your pens to be.