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I've worked up a direct comparison using various image crops from the three super-wide zoom lenses listed below.  The crops used here are the same as the crops used in each corresponding lens review.  This comparison is just for fun as the real differences between each lens may not be very noticeable unless displayed side-by-side as I've done here.  The Sony A580 was used for this comparison, along with a tripod, remote shutter and manual WB.  Bracketed manual focusing was used, with the resulting absolute sharpest shot used as the base for the entire set, at each length.
 

Sigma 8-16mm F/4.5-5.6 DC HSM (only at very bottom)
 
 
Random observations;
 
Best control of flare and ghosting; The two Sigma's, with the Tokina way behind.
Best distortion signature; the Tokina, and a close second is the Sigma 10-20mm F/3.5.
Best focusing accuracy, the Sigma's aren't great, but are adequate; the Tokina is awful.  
Best value for image quality alone; stopped down, the Sigma 10-20mm F/4-5.6, or the Tokina if you don't care about AF.
Best value all around; the Sigma 10-20mm F/3.5 because of the distortion signature, build, and optical quality.

 
Quick comp (13-16mm) between the Sigma 8-16mm F/4.5-5.6 DC HSM and the Sigma 10-20mm F/4-5.6 EX DC at the very bottom of the page, this was added later, as I didn't have the Sigma 8-16mm with the other lenses.
 
 
The blank squares are a result of Sigma's 10-20mm F/4-5.6 smaller maximum aperture not starting at F/2.8-3.5 like the others, it starts at F/4 at 10mm, and F/5.6 at longer lengths etc.  Also, the Tokina starts at 11mm, so it has a slight advantage in resolution at this focal length because the distance to subject was not adjusted accordingly, the other two were shot at 10mm.
 

 

10-11mm centers

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

 Tokina 11-16mm F/2.8

F/2.8-3.5

JUNE2011/sig1020new35ctr.jpg

Intentionally left blank

JUNE2011/tok1116ctr28.jpg

F/4

JUNE2011/sig1020new40ctr.jpg
JUNE2011/sig1020old40ctrw.jpg
JUNE2011/tok1116ctr40.jpg

F/5.6

JUNE2011/sig1020new56ctr.jpg
JUNE2011/sig1020old56ctrw.jpg
JUNE2011/tok1116ctr56.jpg

F/8

JUNE2011/sig1020new80ctr.jpg
JUNE2011/sig1020old80ctrw.jpg
JUNE2011/tok1116ctr80.jpg

F/11

JUNE2011/sig1020new11ctr.jpg
JUNE2011/sig1020old11ctrw.jpg
JUNE2011/tok1116ctr11.jpg

 

The less expensive and slower Sigma 10-20mm F/4-5.6 is a little soft in the centers at F/4, while the other two look great.  As you stop down, the differences aren't so clear, but the constant aperture Sigma and Tokina have the best contrast at all apertures.  Also, the slower Sigma is brighter in these center crops, which makes it seem like it has less contrast.  All images have the same shutter speed with indicated apertures, but I could've backed off a third of a stop on the slower Sigma to match the others, although that won't add resolution.

 

 

10-11mm mid-sections

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

 Tokina 11-16mm F/2.8

F/2.8-3.5

JUNE2011/sig1020new35mid.jpg

Intentionally left blank

JUNE2011/tok1116mid28.jpg

F/4

JUNE2011/sig1020new40mid.jpg
JUNE2011/sig1020old40midw.jpg
JUNE2011/tok1116mid40.jpg

F/5.6

JUNE2011/sig1020new56mid.jpg
JUNE2011/sig1020old56midw.jpg
JUNE2011/tok1116mid56.jpg

F/8

JUNE2011/sig1020new80mid.jpg
JUNE2011/sig1020old80midw.jpg
JUNE2011/tok1116mid80.jpg

F/11

JUNE2011/sig1020new11mid.jpg
JUNE2011/sig1020old11midw.jpg
JUNE2011/tok1116mid11.jpg

 

The mid-sections look fairly close in resolution, however, I do see slightly less contrast on the slower Sigma.

 

 

10-11mm corners

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

 Tokina 11-16mm F/2.8

F/2.8-3.5

JUNE2011/sig1020new35corn.jpg

Intentionally left blank

JUNE2011/tok1116corn28.jpg

F/4

JUNE2011/sig1020new40corn.jpg
JUNE2011/sig1020old40cornw.jpg

JUNE2011/tok1116corn40.jpg

F/5.6

JUNE2011/sig1020new56corn.jpg
JUNE2011/sig1020old56cornw.jpg
JUNE2011/tok1116corn56.jpg

F/8

JUNE2011/sig1020new80corn.jpg
JUNE2011/sig1020old80cornw.jpg
JUNE2011/tok1116corn80.jpg

F/11

JUNE2011/sig1020new11corn.jpg
JUNE2011/sig1020old11cornw.jpg
JUNE2011/tok1116corn11.jpg

 

The Tokina extreme corners are really sharp compared to the others.  There is no clear winner between the two Sigma's, although I do see some color fringing on the fast Sigma HSM lens.  Just a reminder; the Tokina has a slight resolution advantage because it starts at 11mm, the other two at 10mm, so the Tokina has less area to cover.  I didn't adjust the distance.

 

 

16mm centers

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

 Tokina 11-16mm F/2.8

F/2.8-3.5

JUNE2011/sig1020new35ctrm.jpg

Intentionally left blank

JUNE2011/tokina1116ctr28.jpg

F/4

JUNE2011/sig1020new40ctrm.jpg

Intentionally left blank

JUNE2011/tokina1116ctr40.jpg

F/5.6

JUNE2011/sig1020new56ctrm.jpg
JUNE2011/sig1020old56ctrm.jpg
JUNE2011/tokina1116ctr56.jpg

F/8

JUNE2011/sig1020new80ctrm.jpg
JUNE2011/sig1020old80ctrm.jpg
JUNE2011/tokina1116ctr80.jpg

F/11

JUNE2011/sig1020new11ctrm.jpg
JUNE2011/sig1020old11ctrm.jpg
JUNE2011/tokina1116ctr11.jpg

 

All center crops at 16mm look quite close in resolution.  The slower Sigma actually has F/5 at 16mm, but I used F/5.6 to keep the apertures all the same.

 

 

16mm mid-sections

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

 Tokina 11-16mm F/2.8

F/2.8-3.5

JUNE2011/sig1020new35midm.jpg

Intentionally left blank

JUNE2011/tokina1116mid28.jpg

F/4

JUNE2011/sig1020new40midm.jpg

Intentionally left blank

JUNE2011/tokina1116mid40.jpg

F/5.6

JUNE2011/sig1020new56midm.jpg
JUNE2011/sig1020old56midm.jpg
JUNE2011/tokina1116mid56.jpg

F/8

JUNE2011/sig1020new80midm.jpg
JUNE2011/sig1020old80midm.jpg
JUNE2011/tokina1116mid80.jpg

F/11

JUNE2011/sig1020new11midm.jpg
JUNE2011/sig1020old11midm.jpg
JUNE2011/tokina1116mid11.jpg

 

Both the Sigma lenses look pretty sharp in the mid-sections at all apertures, but the Tokina is having problems with contrast, especially at wide apertures.   

 

 

16mm corners

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

 Tokina 11-16mm F/2.8

F/2.8-3.5

JUNE2011/sig1020new35cornm.jpg

Intentionally left blank

JUNE2011/tokina1116corn28.jpg

F/4

JUNE2011/sig1020new40cornm.jpg

Intentionally left blank

JUNE2011/tokina1116corn40.jpg

F/5.6

JUNE2011/sig1020new56cornm.jpg
JUNE2011/sig1020old56cornm.jpg
JUNE2011/tokina1116corn56.jpg

F/8

JUNE2011/sig1020new80cornm.jpg
JUNE2011/sig1020old80cornm.jpg
JUNE2011/tokina1116corn80.jpg

F/11

JUNE2011/sig1020new11cornm.jpg
JUNE2011/sig1020old11cornm.jpg
JUNE2011/tokina1116corn11.jpg

 

The Sigma HSM and Tokina extreme corners look awful at 16mm compared to the slower Sigma, that's a surprise.  Stopping down helps the Tokina more than the Sigma HSM, but they never quite match the sharpness of the slower Sigma.

 

 

20mm Centers

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

F/2.8-3.5

JUNE2011/sig1020new35ctrt.jpg

Intentionally left blank

F/4

JUNE2011/sig1020new40ctrt.jpg

Intentionally left blank

F/5.6

JUNE2011/sig1020new56ctrt.jpg
JUNE2011/sig1020old56ctrt.jpg

F/8

JUNE2011/sig1020new80ctrt.jpg
JUNE2011/sig1020old80ctrt.jpg

F/11

JUNE2011/sig1020new11ctrt.jpg
JUNE2011/sig1020old11ctrt.jpg

 

There isn't much difference in the centers at 20mm, but notice how sharp the Sigma HSM is at F/3.5!  Obviously, the Tokina doesn't go to 20mm, that's why those crops are missing.

 

 

20mm mid-sections

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

F/2.8-3.5

JUNE2011/sig1020new35midt.jpg

Intentionally left blank

F/4

JUNE2011/sig1020new40midt.jpg

Intentionally left blank

F/5.6

JUNE2011/sig1020new56midt.jpg
JUNE2011/sig1020old56midt.jpg

F/8

JUNE2011/sig1020new80midt.jpg
JUNE2011/sig1020old80midt.jpg

F/11

JUNE2011/sig1020new11midt.jpg
JUNE2011/sig1020old11midt.jpg

 

The 20mm mid-sections are about the same as the centers in sharpness. 

 

 

20mm corners

 

 

          Sigma 10-20mm F/3.5 HSM

          Sigma 10-20mm F/4-5.6

F/2.8-3.5

JUNE2011/sig1020new35cornt.jpg

Intentionally left blank

F/4

JUNE2011/sig1020new40cornt.jpg

Intentionally left blank

F/5.6

JUNE2011/sig1020new56cornt.jpg
JUNE2011/sig1020old56cornt.jpg

F/8

JUNE2011/sig1020new80cornt.jpg
JUNE2011/sig1020old80cornt.jpg

F/11

JUNE2011/sig1020new11cornt.jpg
JUNE2011/sig1020old11cornt.jpg

 

If you look carefully, you can see the slower Sigma has a very slight advantage in sharpness in the corners at all apertures, although that wouldn't be noticeable in real pictures.  I see magenta/cyan color fringing in the Sigma HSM crops, look along the rocks at the bottom, and shadow/sun transitions on the tree branches.

 

That's it for this comp, new one below!

 

_____________________________________________________________________________________________________

 

Comparison between 13mm-16mm using the Sigma 10-20mm F/4-5.6 EX DC and Sigma 8-16mm F/4.5-5.6 DC HSM.

 

 

13mm centers

 

 

          Sigma 8-16mm F/4.5-5.6 DC HSM

          Sigma 10-20mm F/4-5.6 EX DC

F/5.6

endof2011/s816ctr13f56.jpg
endof2011/sx1020ctr13f56.jpg

F/8

endof2011/s816ctr13f80.jpg
endof2011/sx1020ctr13f80.jpg

F/11

endof2011/s816ctr13f11.jpg
endof2011/sx1020ctr13f11.jpg

 

13mm mid-sections.

 

 

          Sigma 8-16mm F/4.5-5.6 DC HSM

          Sigma 10-20mm F/4-5.6 EX DC

F/5.6

endof2011/s816mid13f56.jpg
endof2011/sx1020mid13f56.jpg

F/8

endof2011/s816mid13f80.jpg
endof2011/sx1020mid13f80.jpg

F/11

endof2011/s816mid13f11.jpg
endof2011/sx1020mid13f11.jpg

 

13mm corners.

 

 

             Sigma 8-16mm F/4.5-5.6 DC HSM

             Sigma 10-20mm F/4-5.6 EX DC

F/5.6

endof2011/s816corn13f56.jpg

endof2011/sx1020corn13f56.jpg

F/8

endof2011/s816corn13f80.jpg
endof2011/sx1020corn13f80.jpg

F/11

endof2011/s816corn13f11.jpg
endof2011/sx1020corn13f11.jpg

 

Performance at 13mm looks about the same on both lenses, you could go blind trying to pick up minor differences.  Distance from camera to subject; about 70' (21m).

 

 

16mm centers

 

 

          Sigma 8-16mm F/4.5-5.6 DC HSM

          Sigma 10-20mm F/4-5.6 EX DC

F/5.6

endof2011/s816ctr16f56.jpg
endof2011/sx1020ctr16f56.jpg

F/8

endof2011/s816ctr16f80.jpg
endof2011/sx1020ctr16f80.jpg

F/11

endof2011/s816ctr16f11.jpg
endof2011/sx1020ctr16f11.jpg

 

16mm mid-sections.

 

 

          Sigma 8-16mm F/4.5-5.6 DC HSM

          Sigma 10-20mm F/4-5.6 EX DC

F/5.6

endof2011/s816mid16f56.jpg
endof2011/sx1020mid16f56.jpg

F/8

endof2011/s816mid16f80.jpg
endof2011/sx1020mid16f80.jpg

F/11

endof2011/s816mid16f11.jpg
endof2011/sx1020mid16f11.jpg

 

16mm corners.

 

 

             Sigma 8-16mm F/4.5-5.6 DC HSM

             Sigma 10-20mm F/4-5.6 EX DC

F/5.6

endof2011/s816corn16f56.jpg

endof2011/sx1020corn16f56.jpg

F/8

endof2011/s816corn16f80.jpg
endof2011/sx1020corn16f80.jpg

F/11

endof2011/s816corn16f11.jpg
endof2011/sx1020corn16f11.jpg

 

At 16mm, the crops look similar, although in the corners I see a little less color fringing and a slightly sharper F/5.6 crop on the Sigma 10-20mm.  That's it for the comp.