Apart from the obvious differences in focal length, here are the other differences:
1. The Sigma as a built in focusing motor, which means it will autofocus on your camera. Be sure to get the one with "HSM" designation. Tokina 11-16 is a screw drive only autofocus, meaning it will not autofocus on your camera, and will only autofocus on D90 and above. In UWA autofocus is quite useful at times because everything in your VF will look small. Not as easy to manual focus. But a lot of us landscape photographers wannabes use MF anyway. But it is up to you.
2. Sigma 10-20 comes in 2 flavors, one is aperture F4-5.6. Meaning at 10mm, maximum aperture is F/4, and at 20mm, max aperture is F/5.6. The other version is constan F3.5 aperture throughout the range. The F3.5 one is considerably more expensive and the filter thread is 82mm, which is very large and you will have a hard time getting filters for it. Tokina 11-16 is a F2.8 constant aperture lens, meaning it is also very good in low light. So if you are shooting indoors, or city life, it will come in useful. BTW the tokina's filter thread is 77mm, just like the Sigma 10-20 F3-5.6. 77mm is one of the more standard filter thread size for lenses.
You might also want to consider the Tokina 12-24mm lens which has a focus motor built in. So it will do AF on your D40.
Hope this helps.
