Though I only show a few images here, the comments are based on shooting many more images, both real world subjects and resolution test charts. All the images below are 100% crops from the original digital images.
At 12mm you can see a slight softness wide open at f4, which goes away by f5.6. Further stopping down to f8 doesn't really make any improvement.
There's definitely some corner softness wide open at 12mm. Stopping down to f5.6 sharpens things up a lot, and further stopping down to f8 makes another slight improvement.
At 24mm there's again a slight sharpness improvement going from f4 to f5.6, but there's no noticeable further improvement by going to f8.
There's noticeable corner softness at 24mm wide open. Stopping down to f5.6 improves things a bit, but f8 is needed to properly sharpen the corner image.
Chromatic aberration is pretty well controlled. The image above (100% crop on the left) shows the slight green/purple fringing observed at the very edge of the image at the 12mm setting. Below is a similar shot taken at 24mm with a 100% crop shown on the right.
Flare resistance was good both at 12 mm and 24mm. Below are two images comparing the Canon EF-S 10-22mm at 10mm with the Tokina 12-24 at 12mm. In both cases the sun was just outside the frame on the right. Neither image shows excessive contrast loss or flare spots. The difference between 10mm and 12mm in terms of angular coverage is apparent. Results at 24mm were similar.
The Canon lens shows very good center sharpness even wide open at 22mm. You really don't gain a lot by stopping down to f8. The Tokina is very slightly soft wide open, but again very good at f8.
Corner sharpness tells a little different story though. The Canon lens is pretty soft wide open at 22mm and really need to be stopped down to f8 to make the image acceptable in the corner. The Tokina is sharper wide open, but it also benefits from stopping down to f8.
At 10/12mm both the Canon and Tokina lenses are pretty sharp in the center and both show a small sharpness increase if the lens is stopped down to f8.
In the corners, the Canon at 10mm wide open is sharper than the Tokina at 12mm wide open. Stopped down to f8 both improve and show similar sharpness.