Close the valves unless you are in the act of draining tanks.
You certainly don't want to leave the black tank open all the time. It needs to get 2/3 to 3/4 full before you dump to create enough flow to force the poo out. You will end up with piles of dry poo if you leave it open all the time. Search for "poo* pyramid". Lots of reading.
Letting the grey tank fill before dumping gives you water to flush out the hose after the black tank is emptied.