They are private unless you have a balcony at the end of the ship. At the end of the ship there is no end screen. Its irresistible for travellers to look over and on your balcony.
Ihave just come back off the island star and had a balcony cabin.
Each balcony is separated with a thick opaque plastic
shield.The only way you can see next rooms balcony is to
lean over your own balcony and stick your head around
the side shield.
It depends entirely on the ship and the cabin. Buy the Berlitz Book of Cruising which lists every cruise ship in great detail including which balconies overlook others and which are really private.
Totally private on the cruise lines we have been on (Princess and P&O).