Looked at the Chester site.
Open gearbox is a proper "Norton" type with cone of gears and tumbler selection. Ought to have a wider range of threads and feed available, 9 on the Norton box multiplied by how ever many input (or output) gear ratio selections there are. Old style industrial lathes tend to have 3 or 4 input gear ratio variations selected by another lever as well as an overall threading / feed selection. However looking at the web-site picture there doesn't appear to be an extra set of selectable gear ratios or even a threading / feed selector lever.
Closed gearbox is appears to be two 3 speed gearboxes in series giving 9 selections. Again I can't see if there are any an extra set of selectable gear ratios or even a threading / feed selector lever.
So the two machines may well be exactly equivalent with 9 threading or feed selection changes on the machine controls with extra change gears included to extend the number of variations. Seems to be no reason for the two variations. However closed gearbox style with DC drive is the common version of this style of machine so maybe the open gearbox goes with the open belt drive version from a different maker.
Website says the beast is not up to continuous industrial style use. So the motor and / or DC drive is liable to get too hot if used for too long. Its unlikely to have full on overload protection or even some guidance as to how hard you can work it for how long. Best to assume the motor or drive will eventually overheat and blow up if you put it to serious use. Eventually being impossible to define in practice. With a belt drive if the motor does go its not going to be impossible to graft something else on. Probably need an external countershaft but its do-able.
As always the supplier has taken their best guess at a price / performance / capability equation that adds up to something attractive, affordable and useable. Down at this end of the market there will always be some fairly serious compromises so when deciding what to buy you have to be very sure that the compromises are mostly outside what you intend to do. Given that any half decent lathe can be expected to last for many, many years I'd go for the open belt version as if the motor or drive does go down 10 years in the future and spares are unobtanium you will be able to do something about it relatively easily.
Clive.
Edited By Clive Foster on 16/10/2017 11:56:59