I actually visited Barbados some time back... It seemed safe enough however it seemed that aside from tourism and rum production not much is going on there... I think that Barbados has the good fortune of being located close to the neighboring Dutch controlled islands like Aruba and a few others there that are popular cruse ship destinations...Jamaica is down right dangerous and even native people who were born there are hesitant visiting parts of the island outside the city... They talk about going back for a visit however when push comes to shove the trip never seems to happen.
The part of Jamaica tourists on cruises visit are just hotels for tourists. If they want to see the real Jamaica (such as its cities), it would be like being in Harlem. No need to go there to see it. They can see the same thing in South Jamaica in Queens. Or as Chaim once said "South Jamaica, or the South Bronx, or Harlem with Carl McCall here yeah you go through Harlem.".