My company has full milestones on the test map and my character has maxed out skills.

All numbers in the list are the selling prices using the "EMPTY" function in the context menu.

Testing was done with soil, or with the respective material of the construction machine (asphalt, concrete). Capacities can only be compared between the same kind of material, though for asphalt and concrete, most machines tied.
For machines tested with soil, they will have different numbers with sand or gravel, since both have a different price per m³. The capacities still stay the same.

Capacities are also comparable between different vehicle types. So the largest excavator will take on average 11 full scoops of material to completely fill the dump bed of the largest dumper.

Flatbeds With Crane, Dumpers, Asphalt Dumpers, Asphalt Pavers, Concrete Mixers and Concrete Mixer Pumps have been filled using the "Fill" function in the context menu, then the materials sold like previously described.

The Hopper of Concrete Mixer Pumps and Concrete Pumps, as well as Concrete Buckets have been filled using a full concrete mixer and the difference in selling price was noted.

Excavators and Wheel Loaders have been filling the shovel on a working site and empty it into a dump truck. The test was done 3 times and the highest achieved selling price was noted.

EDIT:
I've just found out that loading a truck with soil using a wheel loader on a working site, like in the test, will send about 40% of the shovel capacity into the void. I.e. using the DL 550 yielded ~1700$ per load if the dumper truck stood on the working site, and ~2700$ if the dumper truck stood outsite the working site next to the road.
Since all excavator and wheel loader tests have been done under the same conditions, the relative numbers are still working out and the rating is standing as it is. But the true capacity is not reflected in the numbers right now. I update this when if I have the time.

Update 2024-07-28:
- added Kramer and Liebherr Pack vehicles to the lists
- Added column with DLC to all vehicle lists, since Liebherr has both vanilla and DLC vehicles now

*Note: Front shovel / rear shovel

*Note: Faulty autoloading with soil. Manual loading at gravel plant with highest of 3 was used.

*Note: The hopper can be filled with 250$ worth of concrete, increasing the total carry capacity by 2.86%. Yes, it is this few.

By placing up to 14 large concrete buckets onto a WBUILDER HS7S trailer and filling them up with concrete at the concrete plant, you can transport up to 3.2 concrete mixer loads worth of concrete in one go.
Note that you have to use a concrete pump or a concrete mixer pump (recommended) to fill them up. Filling them under the concrete deposit spot is not possible.
This is only relevant for those few construction jobs where the concrete pumps do not reach the highest spots, and if you prefer to play without the quick refill via functions menu.