First thing, check the port reviews on each port at www.PortReviews.com
. There is extensive information on each one. Also, does your ship actually call in Panama City?
What you do in each port is partly determined by what you want to do. Puerto Limon has great beaches, as does Belize city, but you have to reach to get to them.
Cave tubing in Belize is the favored excursion. What do you like to do?