I've known that LEDs are faster to come up to brightness than Incandescent bulbs, but didn't realize how much different they really were. Looking over a bunch of video, frame by frame (easiest method at hand right now), I see about 0.2 seconds faster, and really 0.3 seconds faster for the LEDs to hit full brightness. The circuit used on the LEDs takes 0.0002 seconds to hit full brightness, from when the brake pedal is touched.
So, lets say it takes 0.2 seconds. Assume you are driving 60 mph on the highway. There are 5,280 feet in a mile. 60 mph * 5,280 ft = 316,800 feet per hour.
There are 60 minutes in an hour, 316,800 feet per hour / 60 minutes = 5,280 feet per minute.
There are 60 seconds in a minute. 5280/60 = 88 feet per second.
88 * 0.2 seconds = 17.6 feet
So, an LED brake light could allow a person to <font color="red">stop 17.6 feet sooner</font> than with Incandescent.
But there is more. I've noticed that folks react alot quicker to the instant on effect of an LED vs. the slow ramp up in brightness of an incandescent. What this equates to in reaction time is unknown to me.
Here is a compressed video, sorry about the loss of frames and poor quality due to the compression, notice how the LED light, the top 3rd tail light comes on faster than the lower two normal incandescent tail lights:
(I had to watch the video about 20 times to get my mind and eyes sync'd to actually appreaciate it)