Assuming this is for road.
I’ve got wheels with both. Supposedly the cup and cone roll better, and they do seem very good.
Cup and cone tends to need a bit more regular care and attention, but are pretty easy to service. Cartridge need less attention and again are pretty easy to service with the right tools (just knock out the bearings and fit new ones.)
If I was getting new road wheels I’d probably go cup and cone again.
Edit: meant to add that I think the main drawback stated for cup and cone is that the shell the bearings run on is the hub itself, so if this is damaged through lack of, or poor, maintenance, then you bin the hub (not that I have had this happen yet.) However with a cartridge you have no such worries and just knock out the knackered bearing and replace.