Is Jamaica or Puerto Rico better for vacation?

This would definitely be a matter of preference. It would probably depend on what activities that you would want to participate in as well as the amenities that you are looking for.
Jamaica has a large number of all inclusive resorts whereas Puerto Rico may have only one or two.
Puerto Rico is a US territory and so you do not need a passport nor would you have to worry about using a different currency.
Both have fabulous beaches, exciting cultures and excellent food. Jamaica depends more on tourism and so the players in the market keep on improving their product daily.