Which port is “better to visit”?

Which flavor is better - chocolate or vanilla?

Split and Dubrovnik are different. Split is more of a real working port city; people who love real cities and hate tourists might prefer Split. Dubrovnik is an amazing, unique old city that is also now a crowded tourist trap. I actually hate Dubrovnik during the day, when there are so many, uhm, cruise ship tourists in town, but at night, when the crowds leave, it's just magical. Split sure gets tourists too but it seems to be less of a tourist trap, a little more real - but also somehow much less significant than Dubrovnik. When I returned to Croatia a few years after my first visit, I returned to Dubrovnik not to Split.

Some people prefer one, some the other.

Both are different amd unique in their own way, it’s like comparing apples and oranges.
Dubrovnik is a very well preserved late medieval town with amazingly intact and massive city walls. It very much feels like you are transported back to a specific period in time (or to Kings Landing).
Split is quite different in that regards, since it is a total mix of buildings from many different periods. It’s old town is essentially a city buil in the remainins of a Roman palace. Personally I find it fascinating to see how the old roman buildings have been build upon and incoorporated into the city over the last 2000 ish years.

I've stayed in both Split and Dubrovnik. While I really enjoyed both, I slightly favor Dubrovnik. Part of the reason is that I enjoyed the day trips I took from Dubrovnik, but that would be less of a consideration on a cruise stop. Another factor that might be important to some people is that Split is relatively flat while Dubrovnik has a lot of steep stepped streets. The flat section of the walled Old Town is relatively small, which adds to the feeling of Dubrovnik being crowded when large groups arrive. All that said, I don't think you'd be disappointed with either choice.

Like most answers I agree you can’t go wrong with either city. Split is flat which makes a difference, and is more open so it will seem less crowded. Having been to both, i would choose Split. PS, Also better shopping.

Both were great, but I wasn't on a cruise - and really made a point to schedule around cruise ship crowds. There are websites for that.

In Dubrovnik, you can walk the walls, wander the back streets, and It's a lovely place. We did some fun kayaking and a bike tour with wine tasting. I did not really enjoy the ride up above the city - very crowded for a very crowded view.

In Split, you can go down under and see the old structures underneath the palace, go visit the archeological museum outside of the palace (a reasonable walk) and also do a bike tour that goes up to a park to overlook the city, if that's your kind of thing. I would probably be most likely to go back to Split, maybe. Tough decision.