The Captain(s) do seem to have a preference on where and which direction to dock, but there is no sure way of knowing which side of the ship will be dockside at any port. The ports schedule, weather, maintenance needs, and lifeboat exercises seem to be the biggest determinates on how the ship docks. But I know such things as a scheduled photo or video shoot can also determine how the ship may be positioned at any port. The only one Ive never seen changed is when the ship(s) are at Port Canaveral, Ive only seen them with the starboard side to the dock.
That being said, it seems like each side gets equal time against the dock and depending on the port you may or may not get a better view from dockside.
So, I think the answer to which side is better is going to be a personal preference, and could be different on every voyage. Of course DISers will be glad to share their preferences with you, but in the end I think both sides have equal appeal.