Sigma has 2 versions. The 10-20 f3.5 EX DC HSM and the 10-20 f4.5-5.6 EX DC HSM. The Tokina has a constant f4.
The Sigma has Full Time Manual Focusing, quite a nice feature. However, the f/4.5-5.6 variant has a curved focal plane.
The Tokina has solid built quality, but has higher amount of chromatic aberations.
However, if you'd do landscapes, the Tokina 12-24 or the 10-20 F4.5 -5.6 would both do. To me, the Tokina is sharper though.
Sigma has 2 10-20s - one is f3.5 HSM, the one being f4.5-5.6 HSM
The siggy f4.5-5.6 has a significant curvature of field, and strong barrel distortion at 10mm with a rather unusual and complex pattern, localized mainly towards the corners of the frame. Sharpness is good at center, but generally poor at corners.
The siggy f3.5 has rather strong barrel distortion at 10mm too, but far more uniform and easier to correct. Sharpness is generally similar to f4.5-5.6's.
The tokina 12-24 has strong barrel distortion at 12mm. Sharpness is generally good with this lens, but CA levels are very high.
If you need FTM, or very wide angles, and don't mind stopping down to get better corner to corner sharpness, the sigma 10-20 f3.5 is a good choice.
If you want good sharpness wide open but don't mind high CA levels, the tokina is a better choice.
If you don't mind considering other choices, there's sigma 8-16 - it performs far better than both sigma 10-20, but doesn't take filters.
The tokina 11-16 is good too - there's a constant f2.8 and bags of edge to edge sharpness, but comes at a price of limited focal length and high levels of CA
That was a long, long time ago... since, as also mentioned above, Sigma has also another 10-20mm, Tamron has a 10-24mm and Tokina has the 11-16mm.
Basically, if you want to take filters, and not a fisheye and on an APS-C, go for...
(a) the Sigma if you love a super-wide view (nothing else go wider but for a debatable QC)
(b) the Tokina 11-16mm if IQ is the overidding factor (but Tokina is infamous for its CA)
If you ain't sure, the older version of the Sigma 10-20mm and the Tokina 12-24mm can be had "relatively cheaply" now in our own ClubSNAP classifieds. You don't loose much there.