LED screens ARE LCD screens, it's only the backlight source that's different, at least until OLED takes over.
The major difference is size, LEDs are very low profile and can be distributed around the backlighting area in order to balance the brightness over the viewing area. Fluorescent tubes need higher voltage (usually an inverter per tube) and are larger. There is also an issue of dynamic brightness control, CFL brightness is relatively slow to react in comparison to LEDs and can only be achieved over the whole screen area. Because LEDs are quicker to change brightness the backlight level can be adjusted in time with the picture content to improve the contrast ratio. Finally, from a manufacturers point of view, LEDs can be fitted to a PCB but fluorescent tubes require special mountings so are more expensive and labor intensive to produce.
Brian.