I prefer starboard because on each of our cruises - (ship docked the same way each time)
Our view at the Port is of the loading and unloading of the ship, we faced the lagoon at CC, on the Eastern we faced the water and saw the boats at St. Thomas and St. Maarten (the opposing view is of the mall and mountains) - on the Western, we were able to see the city at KW, no difference at Grand Cayman since we have to dock in the water and be tendered in, and at Cozumel - we faced the water.
So it all depends (1) how the ship docks and (2) what you'd like to see.
Rae