With the Fusion Builder Live Editor, you edit your content directly on the front-end. You can see your layout as you build it, and any changes you make update immediately as you make them.
Additionally, with Fusion Builder Live, you have direct access to the Fusion Theme Options, as well as the Fusion Page Options, on the same page, as you build. This can speed your workflow significantly.
In most other ways, the two builders are the same. There are interface and workflow differences, but they both use the same Container, Column and Element structure, and controls. The content that both builders generate is also identical, and so there is full compatibility between the two builders. You can even toggle the Wireframe view in Fusion Builder Live, which essentially is the back-end builder in the front-end interface.
So with Fusion Builder, we have now just doubled your options, giving you two ways to build your website. Welcome to the best of both worlds!