For those seeking a top-quality, show-winning restoration, the type which many in the hobby refer to as a "Pebble Beach quality" restoration, the body must come off. Even if you want just a good-quality restoration, but are not seeking a flawless end result, there are still many advantages to removing the body from the frame.
Body-off restorations mean just that: The car's body is unbolted and completely removed from the chassis, or frame, whichever you prefer to call it. Technically speaking, it is wrong to use this term when referring to unibody cars such as AMCs, Sixties-era Chryslers and MGBs. For these types of cars the correct term would be ground-up restoration.
With the body removed, you will be able to strip the frame of its existing finish and thus be better able to inspect it for cracks, broken welds and rust problems, which can have a detrimental effect on your car's handling and your own personal safety if not found and repaired.
Refinishing the frame with modern, durable primers and paints will ensure it will last for decades to come. The exposed frame will also allow you to easily install new brake and fuel lines for increased safety and reliability, and to clearly see if any bolts, nuts or clips need replacement. It will also provide unimpeded access for you to accurately and solidly install the exhaust system without any chance of it banging into the frame later on.