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The sigma 10-20 is a linear projection type and has a smaller angle of view.
The Tokina 10-17 is a circular projection type (fishey) and provides a very wide angle of view. It has high distortion, except lines which ecxactly crosses the center of the picture. The distortion is not a fault or failor but a result of the wide angle of this lenses. For understanding, imagine a flat map of the hole earth. You will see the longitudes and latitudes are all distorted except these which are crossing the center e.g. the equator.
As I know Sigma also offers a circular lens.
Tokina also offers a linear lens (Tokina 12-24).
What kind of lens to use, depends on the requirements. Super wide angle or no distortion. Both are not possible. I have both.
Sorry for my englisch. I hope you understand what I tried to explain.
our English is far better than my Austrian would be.
Have a good day!