You are right in that HG doesn't explain enough to compare/contrast the two. The crane is clearly designed to pick up cargo internally/externally and then deposit it outside the ship, either on the ground or a vehicle. But it doesn't list it's unloading speed.
The loading belt is specified to replace 10 crewmen who would be manually unloading, or 25 crewmen at TL12. It mentions the TL12 version can use high-powered magnets to propel cargo containers (an idea I find a bit silly, not to mention dangerous for the crew - especially those with metal piercings! :mrgreen: ).
I could not find any data that references how fast a cargo crane can move an object. The cargo crane specifies it's strong enough unload 32 or 65 ton containers, but not how fast, or how many crewmen are used.
The loading belt description is almost comparing it to old-fashioned freighters where stevedores did all the work except for lifting. Basically you are left to make it up on your own. I checked GURPS and didn't find an explanation either of unloading speeds. I can tell you that in the real world a container can be loaded/unloaded from a ship at speeds of up to 64 containers/hour. But that may be a bit too fast for your cargo vessel. However with modern cargo moving equipment you still are able to move a container onto a flatbed in minutes. Cargo belts today usually handle solid-type cargoes (grain, coal, etc), and aren't used to move containers.