First, despite the marketing hype, technically there ain't no such thing as a "white" LED; typical contemporary (since the latter '90s), current-production commercial "white" LEDs in reality are Gallium Nitride-based (GaN) blue emitters (450-470 nm wavelength) the "lens" or package of which has been doped with a scintilator (sorta like a phosphor such as those which povide the luminance and chrominance of a CRT, but different), usually based on a combination of Cerium - Ce, Yttrium - Y, Aluminum - A, and Garnet - G, which upon excitation by the emmitter overlays the blue output with a broad spectrum bias centered on 580 nm (yellow), with variations of the composition of the doping resulting in shifts of apparent color temperature varying from warmish slightly yellow to cooler bluish (see:
Variations of light characteristics of white LAEDs. Due to the way the human eye responds to the various wavelengths of light, the emmitted output
appears to be white when viewed directly, however, the reflected illumination characteristics render red and green objects illuminated thereby noticeably, often objectionably, less vivid than is the case when such objects are illuminated by actual full spectrum white light (see:
Raman Scattering. Earlier attempts at producing "white" LEDs involved the use of Near Ultraviolet emmitters, with other package doping, but were unsuccessful as the effect of ultraviolet radiation negatively impacts the transparent plastic package, or "lens" in which the actual LED semiconductor is embedded.
That said (and no doubt more than you wanted to know), while the illuminative efficiency of such emmitters individually is not high, ganging multiple emmitters, whether in the same package (again, the "package" is the transparent envelope or "lens" in which the actual light-emmitting semiconductor diode is embedded) or fabricating suitably configured arrays of emmitters does geometrically increase the effective light output. Current production Solid State Lighting Devices are of the latter type, arrays of many individual emmitters configured as a lamp assembly. Electrical efficiencies are on the order of around 30-35 lumens/watt, substantially greater than that afforded by incandescent illuminators which average from around 15-16 lumens/watt for conventional tungsten lamps to around 20 to 25 lumens/watt for halogen lamps, primarily due to the fact LEDs do not generate anywhere near the heat, or infrared, output per input watt as`compared to conventional incandescent illuminators.
While in terms of lumens-per-watt and lumens-per-unit-of-cost, florescent lighting still is far and away at the head of the pack, at least for today, ongoing LED illumination research and development promises near-term market feasability of substantially higher electrical efficiencies, though production considerations will allow both florescent and incandescent illuminators to enjoy considerable cost-per-lumen advantage for the foreseeable future.
The short version: "white light" LED illumination, presently at around 30 to 35 lumens-per-watt efficiency, is an emergent technology with great promise, though there are yet significant hurdles to be overcome before it achieves a cost-benefit advantage over conventional florescent and incandescent illumination in general lighting applications. That day certainly is coming, but it ain't quite here yet.