LEDs have far superior color purity than any phosphor; they are almost perfectly monochromatic due to quantum emission. Phosphor-based technologies are CRT direct view, CRT rear projection, plasma, and SED.
The image below is excerpted from p.3 of an interesting paper
(PDF) by NEC on their LED-backlit LCD2180WG LCD:
Comparing CCFL to phosphor output spectra, we next turn to Colorimetric Characterization of Three Computer Displays (LCD and CRT)
(PDF). This valuable paper is one of the only (online) to provide graphic phosphor spectra; the main subject is a comparison of the various characteristics of three displays: an SGI 1600SW LCD, IBM 'prototype' LCD and a Sony GDM-F500 CRT.
Remember, the following graphs are normalized spectra, so look only at the dark dotted line, not the solid, light dotted or light dashed lines.
First, let's look at the red channel:
Sony GDM-F500 CRT Red Emission Spectrum
SGI-1600SW LCD Red Emission Spectrum
Both CRT and CCFL emitters do well with good purity. The CCFL emitter is slightly orange compared to phosphor. Phosphor wastes energy with a spurious emission band in the near-infrared.
On to green:
Sony GDM-F500 CRT Green Emission Spectrum
SGI-1600SW LCD Green Emission Spectrum
This is where phosphor and CCFL emitters part company. The phosphor emitter shows characteristic awful purity, with a huge hill-shaped emission band whose peak is centered on 'green'. The visible yellow-greenish color of CRT phosphor is due to the slowly-decaying slope to the right, persisting long into the yellow and even including some orange. In contrast, the CCFL emitter maintains a consistently narrow output.
Finally, the blue:
Sony GDM-F500 CRT Blue Emission Spectrum
SGI-1600SW LCD Blue Emission Spectrum
Again the CRT blue is a disaster, only slightly less than its green. CCFL blue has significant broadband emissions in the blue-aqua region, with a sharp band in the aqua. Of the three primaries, CCFL phosphor's color purity is worst for blue, and very good for red and green.
Comparing CRT to CCFL emission spectra, the CRT loses worst in green, not so badly in blue, and produces a significantly deeper and also purer red than CCFL.
Both plasma and Cold Cathode Flurorescent LCD backlights use UV (ultraviolet) excited phosphors to produce light. It might be expected that plasma will have similar output spectra and purity to CCFL, but then again the formulations may be different.
Finally, comparing LED to CRT and CCFL phosphor spectra, LED clearly wins.
Spectral purity is achieved by making the three primary emission lines as narrow as possible, and locating them in the correct three frequencies. This allows colors to be as pure and saturated as possible. So red should have an infinitely thin line between 650-670nm (user preference), green at 550nm and blue at 425-440nm.