Get both. [6] Seriously, as others said, they're very different.
The 17-40L would be more of a "general purpose" or "walking-around" lens, the equivalent of 27-64mm on a full-frame camera. That would be an improvement over your 24-105mm (equivalent to 38-168mm)--a factor of 24/17 = 1.4. (In other words, the 17mm will show a subject at the same size as the 24mm will at 1.4x the distance.) It's a minimal "general purpose" lens due to the narrow zoom range, but isn't too expensive. However, as Bryan says, it's not a good "people" lens for portraits, unless you discipline yourself to back off and crop later.
You might consider the EF-S 17-55mm f/2.8 IS lens--longer focal length range (equivalent to 27-88mm), wider aperture (great bokeh!) and IS--plus possibly better image quality. (See Bryan's reviews.) It is more expensive, however: $1030 vs $700 at B&H, though I got a used 17-55mm for $800 on eBay and am very pleased with it. A bit cheaper, yet, is the EF-S 17-85mm f/4-5.6 IS ($515 at B&H), my second "good" zoom. The image quality is very good (watch for barrel distortion at the low end, however) and it has IS and a 5x zoom range (27-136mm). It is slower than the 17-55mm lens, but not much slower than the 24-70mm. The 17-85mm IS is the lens I used to keep on my 30D. (I'm leaving the 17-55mm IS lens on now to force myself to use it.)
The 10-22mm is equivalent to the 16-35mm on a full-frame camera. Compared to your 24-105mm, at the low end, the ratio is 24/10 = 2.4, considerably different. It's not a general purpose lens, at all, but a super-wide-angle that may be less--or more!--useful for you, depending upon what you want to do.
Contrary to popular belief (well, MY popular belief before I wised up), a super-wide-angle lens is not really for "getting it all in." Landscapes with such a lens can be pretty boring, plus you'll get a LOT of foreground and sky. Sometimes, you may want that--e.g., you want to show a desert landscape that looks endless. My more common use is to get really, really, really close to the subject, without magnifying the image, as a macro lens would do. This gives a very different perspective than taking the subject from much further away with a longer lens.
Note: the lens focal length has nothing to do with perspective. Perspective depends entirely upon the relative position of the viewer and the subject. To prove this, set up a shot with a wide-to-tele zoom (e.g., the 17-85mm Canon) and take the same scene at different focal lengths. Then crop the shots taken at shorter focal lengths so that the subject is the same size as the longest. The shots will be identical (except for the number of pixels, which you can correct by scaling them all to the same size). What does change the perspective is the distance to the subject. To "fill the frame" with a 17mm lens, you'll have to be at 1/3 the distance that would fill the frame with a 50mm lens; for 10mm, you'd have o be 5x the distance. We don't notice that exaggerated perspective so much when we look at something up close, as our brains compensate. A photo doesn't give us the clues that the subject is very close. (That's also why telephoto shots look "flat"--our brains tell us that the image is only a few feet away.)
I don't have the Canon 10-22mm, but I do have a Sigma 10-20mm. Here are two examples, both taken at 10mm.
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This was taken maybe 10 inches from the apple in front. The two apples were about a foot apart, but it looks like a lot more because of the perspective, which also makes the apple look rounder.
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The second was a bit further away, but still very close. If I had backed off several feet to use a longer focal length, the perspective would have been very different.
The best thing to do would be to borrow both lenses and try them out for few days.
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