For landscape astrophotography you need a wide angle lens that can gather as much light as possible. Practical light gathering ability is determined by two factors in this scenario: the aperture (and transmission) of the lens and the exposure time. You'd usually want to avoid star trails, so exposure time is limited by how wide the lens is. The wider the field of view the longer exposure can be without noticeable star trails. Ignoring the corners of the picture, the maximum exposure time is going to be inversely proportional to the focal length.
If
a denotes the f-number of a lens and
f denotes its focal length, then lens 1 will be
x stops better than lens 2 where
x = log_2 (
f2/
f1 * (
a2/
a1)^2)
Comparing 11 mm f/2.8 with 20 mm f/1.8, we get that the 20 mm is log_2 (20/11 * (2.8/1.8)^2) = 0.4 stops better than the Tokina. It's 1 stop worse due to being less wide but more than 1 stop better due to a smaller f number. In other words, you'd have to use 2^0.4 = 1.3 times higher ISO with the Tokina.
For more precision, you might want to look up the actual transmission ("T-stop") of the lenses on DxOMark. For example, the Nikon 10-24 mm f/3.5 transmits
less light than the Tokina 12-24 mm f/4 even though it has a smaller f-number. This information is not yet available for the 20 mm f/1.8
Light transmission ability is not everything of course. Another important optical characteristic is
coma, which determines the shape of stars. They won't typically look like points in the corners. You can look this up on lenstip.com:
Here's for the 20 mm
Here's for the Tokina
You can see that on a D7100 (APS-C sized sensor) the stars will look more point-like with the Nikon than the Tokina.
Of course the big disadvantage of the Nikon compared to the Tokina is that it's not nearly as wide on a D7100, and won't be able to show as much of the Milky Way. Not to mention is costs more and it's really designed for larger sensors.
. So 20's great across-the-frame sharpness, no complex distortions and speed make it a great candidate.