The SpaceX Superheavy Starship will be taller and have more payload capacity than the Saturn V.
The fully reusable rocket could have a per flight cost of $2-5 million for its 150 ton capacity.
There is currently a payload size of 18 meters height by 9 meters wide for 1000 cubic meters of volume.
There will be a taller payload faring option with 22 meters in height. This could provide 1200 cubic meters of volume.
The current volume of the SpaceX Starship would match the International Space Station. The taller faring would provide a payload volume that is 20% more than the ISS.