There are a lot of questions lately about left/right balconies that just don't stack up. What difference does it make when you enter the Med? Are you expecting to be seeing the coastline at close quarters? A cruise is a round trip so the sun & shade will have equal benefit. The only advantage is on an East to West one way journey where the sun will be on the port side & to change for an overlooked balcony doesn't appear to be the best idea.......Wilba.
I would have thought that there is a slightly higher chance of the balcony on Aloha deck being overlooked from one of the suites above than the one on Caribe Deck. You will get more movement in choppier seas in the Aloha Cabin. You have not said which itinerary but I am assuming the cruise to Rome and back. As wise Wilba says the trip down to the Med and back means the ship is travelling south then north so no real balcony/sun advantage, going to Rome the starboard side (right) gets the sun, coming back the port (left) gets it. Biscay can be the bumpy bit. ..... Neil.
We have had cabins on Caribe deck on both Island and Crown Princess. The balconies are partially overlooked because they are larger than those (standard balcony cabins) on other decks. I have to say that it has not bothered us in the least. The balconies on Caribe deck on Grand Princess are also larger and will, possibly, be overlooked.
Just make sure you are not under the spas these are drained at about 10.30 at night and it sounds like a train thro the room .