I am big on LED bulbs and have a few 3 way bulbs (OK more than a few) (although lately I've taken a liking to Phillips Hue remote control dimmables). Anyway the 3 way LED bulbs seem to light med-high-low as you switch through. Traditional incandescent are low-med-high. Why the change?
It may be just how they're wired, but it could be due to the electrical properties of the LED chips themselves.
I prefer incandescents for the most part. The yellowish light they give is more "natural" to the human eye. They were designed this way originally as the color light the early incans put out was very similar to candlelight (which was the standard for centuries).
Flourescents tended to be more bluish, and - although more energy efficient - that off natural light kinda put people off at first. Now with better internal coatings they can make the like more "natural". But the use of mercury vapor kinda negates the more enviornmentally friendly image they've pushed.
LEDs are nice for portable devices as their current draw is so low but most don't put out nearly as much light as the other two. Judicious design and precise manufacturing allow alot of chips to be crammed into the available space and now the light yields are high enough to compete in the residential markets.
I like incans around the house, flourescents for outside lighting (the lower heat output makes the fixtures last alot longer), and LED's for flashlights.