We have done both but prefer port aft. Always a balcony. Always with cabins above and below.
I'm not so much stuck on left or right, but definitely pref aft.
Port gives us the evening sunset on the way home and that is nice to see and photograph.
On many of our cruises it is the port side that faces land when docked so we get some nice views there too.
All that said, this time (29 Sep) we are starboard, but at the very last cabin (5293 on the Pride) since we needed 3 balconies in a row for family to help celebrate our 50th anniversary..