That's the big question. If perceived brightness is anything like perceived loudness, twice the nits wouldn't appear twice as bright. With sound it actually takes about 10 times as much power to produce something that's perceived as twice as loud, and twice the power is only 3 decibels louder.
Also, from what I've read it sounds like the anti-reflective nature of the screen might be just as responsible for improved visibility in daylight as the actual brightness of the screen (it almost acts like a sunshade so that the image on the screen doesn't have to compete as much with sunlight reflecting off the screen).
Between both of those, there might not be nearly as much difference between the 1000-nit and 2000-nit
CrystalSky's as there is between the a 1000-nit
CrystalSky and e.g. an iPad.
FWIW I did a quick search and found this video comparing displays with various brightness levels side-by-side: