The shortbed has a lot more 'camper' in the tail/skirt area (the space between your trucks tailights and the rear wall of the camper), since more of it hangs off the back of the truck than with the long bed version. That's why you can get a generator with the short bed version and you cannot with the long bed version.
I would suggest that for most people you could not put a short bed model on a long bed, or one wouldn't want to, but I suppose anything is possible for someone willing to deal with the circumstances.
2014 Four Wheel Grandby. Rides on a 2007 Ford F350 6.0 SRW Torqshift