Comparing the ultra-wide, crop sensor camera lenses is an extremely difficult task, so I’ll put the summary first: they all deliver excellent image quality and you can’t go wrong with any of them. To my ‘just taking pictures’ assessment they are all excellent. There are some differences though, so I’ll try to point those out so you have a better chance at choosing the one that’s best for you.
The Sigma 8-16 f/4.5-5.6 is the widest (and remember, 8mm is 20% wider than 10mm, so it’s a very real difference). Not quite as sharp in the corners as the others, and lower maximum aperture, but it’s really pretty good, especially considering it’s the widest of the wide.
The Canon 10-22 f/3.5-4.5 is arguably the most flare resistant, the smallest and lightest when that’s important, and has low distortion. It’s also the most expensive and vignettes a bit. I like it a lot, though, and often find myself preferring it because of its small size.
The Sigma 10-20 f/3.5 has a bit more distortion than the others but delivers very nice images and is also built much better than the Canon 10-22. It does everything well and probably is the best value of the bunch.
The Tamron 10-24mm f/3.5-4.5 Di II VC HLD for Canon is the least expensive of the bunch and has the longest zoom range. It actually has less barrel distortion than most of the others, but a bit more chromatic aberration (purple fringing) and perhaps a bit more vignetting. But none of these are severe and the larger zoom range often comes in handy.
The Tokina 11-16 f/2.8 Mk II gives you the widest aperture if you’ll be working in low light (with ultra wides, depth of field is rarely an important point), but it’s a bit soft at f/2.8, so the aperture advantage isn’t huge (I usually shoot it at f/4, if I can, to get it sharper). It has very little vignetting and distortion, probably the least of the group. Unfortunately, it does show quite a bit of chromatic aberration and is known to flare at times. But if you need f/2.8, this is your only choice, and it’s not a bad lens at all.
But like I said above: they’re all excellent. We hardly ever get anything but happy comments about any of them.