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Let's look at the different claims one at a time.
"One company says to replce the duct work becvause the newer units oush so much air it would not hold the metal ducts."
Complete nonsense but there is a kernel of truth there if only that your system (particularly the AC) would function better with properly sized ductwork.
"The third company says the duct work would sweat and cause leaking in the ceiling?"
The ducts must be insulated if you want AC. You will hae problems with condensation (sweating) on the ducts that are out in the open and exposed to the air. If a duct is buried in a wall condensation is possible but a lot less likely. Condensation happens when the warmer moist air in the room comes in contact with the cooler metal duct surface.
"The other company says the duct work is fine."
No way I can know that without seeing your system but AC could work as long as you insulate the exposed ductwork.
I'd recommend that you insulate the ductwork at a minimum. The ducts buried in the walls can stay but it also might be worthwhile to replace the main exposed ductwork since it's not likely to be sized for a modern system.