Hi, I debated a similar question a few years ago, but in my case it was 24-105 vs. 17-55/2.8 (there was no EF-S 15-85 at the time). I ended up with the 24-105 primarily because I wanted the long end.
Later I added EF-S 10-22 and was very happy with the 10-22 / 24-105 combo for years. I’m sure you would also like the 24-105 paired with your Tokina. But…it’s kind of a hassle always having to bring an extra lens. If I had known what I know today, and if the 15-85 had been available at the time, I may have chosen the 15-85 over the 24-105. (I’m not sure because I really don’t like a varying maximum aperture design.)
As I see it the optical performance (IQ) isn’t the differentiator between these lenses - both are very good. The 24-105 has an obvious advantage if you would get a FF body some day, but considering the camera you have today I would compare them like this:
EF 24-105: Constant f/4 through the entire range may not be the fastest but is fair enough. It has some more reach, but the extra reach isn’t enough for outweighing the poor wide angle. (15-85 mm is a much more versatile range.) Paired with a wide angle zoom the 24-105 works nicely, but then there will be lots of lens swapping. (And to be able to do that you always have to bring an extra lens.) The EF 24-105 is a really solid high quality lens - it feels great to use.
EF-S 15-85: It has a perfect normal zoom range but the f/3.5-5.6 thing is annoying. If you don’t have a problem with the varying maximum aperture it’s the natural choice. Of course it depends on your shooting style, but I would personally find it difficult not to have the range 17-23 covered. For me that's a quite common focal length range (on my 7D) and the versatile EF-S 15-85 covers it.
Good luck with a tough decision…





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