Most people who decide to tear down a home have actually purchased the home with that specific intent. They have usually made all the arrangements in advance, which makes the entire process of teardown and building easier, and usually more financially viable. Both options may work for you, but it really depends on a lot of different factors. A few that come to mind are the actual goals, wish lists, and objectives you would have in a remodeling project vs a building project, your budget and ability to finance if necessary, and the values and ages of the homes in your neighborhood.
Contact a builder or realtor who is active in your neighborhood. They will be able to help you determine if building a new home would be a wise investment, or not, based on the other homes around yours. They will also be able to give you some information that will give you an idea of how much you could wisely invest into your home should you decide to remodel it.
In addition, a home builder can also help you to review your options. Since you are trying to decide between remodeling and building it will help if you talk to contractors who do both, of which I am one and would be happy to help. When it comes to selecting a builder, do your homework. Check references, testimonials from other customers
An issue in Florida concerns FEMA in Flood Zones. If you remodel more than 50% of the Appraised Value within the past 5 years, you are required to raise the slab to the current flood height requirements. An addition may also be required to meet the new flood elevation requirements. Check with a good local GC and the Building Department and make sure you have ALL of the info or it could cost you a lot of headache and money.