A Florida LLC can be managed in two ways: by its members, or by managers (or a single manager). There is no inherently better choice. Each LLC must determine its own needs and what management structure will suit its business best.
When you form a Florida LLC, you must list the members or managers who are responsible for managing the company on your Articles of Organization. You are required to include their names, their addresses, and their title (either Member or Manager).
The actual breakdown of management, however, is determined in your Florida LLC Operating Agreement. It is in your governing document that you will determine the management structure of the company, who management will be vested in, and what the duties of management will be.
It should be noted up front that a manager can be either a member or a non-member third party. There is no restriction. As well, a member is not required by law to be a manager.