I'm not sure why you think the 10-22mm isn't a pretty darned sharp lens across the frame... or that the Tokina 11-16mm is much better. Compare for yourself
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Do you have a "protection" filter on your 10-22mm? If so, that might explain the softness toward the corners you are seeing. If using one, try the lens without any filter and see if there's a difference.
You might already be aware, most lenses also give the best results at their middle apertures. Try using f8 or f11 at the wide end of the zoom, if not already doing so, whenever light allows.
Sharpness isn't the only consideration... The 10-22mm's biggest "problem" is some vignetting at the largest apertures, which can be controlled in camera with Peripheral Illumination or in software in post production, or simply by stopping the lens down to the middle apertures. The Tokina shows less vignetting at the same focal lengths and larger apertures
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On the other hand, the 10-22mm minimizes flare far better than the Tokina 11-16mm
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The 10-22mm's hood is so large and shallow it doesn't seem like it would have much effect, but it does. It's often important to use it to help prevent flare and help keep colors nicely saturated.
There are many ways to sharpen images... I use Lightroom and Photoshop... first applying a bit of sharpening when converting RAW images in Lightroom. (Note: It depends upon the camera, too. I shoot with 7D mostly, which need more sharpening than some other cameras... I also use 5DII, and don't apply any more than default sharpening initially, when converting RAWs). I then finalizing sharpening as a very last step in Photoshop, once the image has been completely optimized and sized for it's intended use.