Should I go to the Grand Cayman or Jamaica?

Should I go to the Grand Cayman island or Jamaica? I do not want to spend a ton of money but I do have some to spend if that makes sense. I will be going in May which place has the best weather and most activities. A key factor in where I go is the beach which place has the best beach? I want to do activities like scuba, snorkeling, maybe fishing, sight seeing etc. Which place would you recommend. If Jamaica where at in Jamaica and is Jamaica dangerous? I heard they have the second highest murder rate in the world scary...