Sorry, but I am not sure you know what you are talking about. I do not mean any offense by this, but what you stated is confusing and not entirely true. I think you are thinking of OLED maybe? Where each pixel is an LED.
When it comes to computer monitors, they are all LCD's (With the exception of OLEDs, but they are still rare and small). You have two back lighting types. Either edge lit LED, or edge lit Florescent for standard LCD's.
LED back lighting is pretty much superior in every way. Although this greatly depends on the quality of the display. LED back lit will not yellow over time to the extent that florescent back lit displays will. Brightness levels depends on the display quality, and can be very bright in either case.
Personally I see zero reason to go with a florescent back lit display.