Hello Jeff,
Cris has highlighted probably the most important factor, the potential for the A frame type movers to loose grip.
Its one thing for the mover to hold a caravan in position on a slope, but does it have the grip to stop it if it is already coming down a slope? As a guide, if you could not stop it by hand, it is highly likely that the mover would also have difficulty.
I would like to add a few further points to consider:
If you are having some difficulty moving your caravan at home, it is quite possible that you may find a similar situation on site where some assistance would be helpful, or perhaps you arrive on site when it is dry but need to move the caravan off in the wet. At these times a mover would be advantageous.
The A frame type movers usually need to be removed when towing, so if you were to take it with you, you need to consider where it will be stored, and how easy it is to fit and remove.
The chassis type movers always have better grip because they have virtually the whole weight of the caravan on the driven wheels. They are always there ready to be used, and don't need to be carried or stored elsewhere.
Chassis type movers do tend to be heavier than A frame type, so they detract from the payload of the caravan, but a A frame drive with its own battery could be heavier than one o the chassis mounted ones!
Look through this forum, use the search facility, and I think that you will find that almost universally those caravanners who have a chassis mount one swear by their effectiveness, and there are several instances where contributors have told how they have replaced A frame drive units with chassis mount ones for the reasons above.
A frame drives are fine on smooth hard level surfaces, but they can struggle on slopes, sometimes with dangerous consequences.