The real answer is 'depends'.

White LED usually consists of phosphor (react with the chip emission) layered on a diode (such as GaN, which emits violet light 405nm) that's why they are white. The phosphor gets activated by the light from the chip and emits another wavelength of light, hence different colour in a mixture to produce white.

Wavelength of White LED are such shown below (lifted from Wikipedia):

Wavelength that can be perceived by normal trichormatic eyes shown below:

As you can clearly see, White LED has already covered up most of the spectrum leaving only the near 400nm wavelength uncovered. The other problem might be uneven wavelength brightness, which means even though the light looks white, the object tends to have a unnatural blue/green tint as shown in this video. The technical term for this is called low CRI.

Also, the brightness of such LED will somewhat suffer due to inherent Stokes shift problem. Manufacturers have invested to improve the GaN system such as shown below.

Numerous technologies for LED has emerged but availability on the market is not really known.

Then what about bulb you say?

Well, fluorescent light works with the basic principle as the LED, which means they too can have low CRI, albeit a lot brighter.

What you are comparing, I assume is incandescent halogen lighting. Halogen light have two main disadvantages, being really hot when using and very inefficient. The light they produce have great CRI (not to say the best), but are definitely one of the strongest (halogen lights on car, anyone?).

---- Edit ---- Did I mention plasma lighting? They are quite efficient and have very good CRI. This is because they mainly heat gases up (argon/neon or more) into plasma and turning them into a blackbody radiator.

Look them up.