I absolutely love my 18-135 IS Nano when i use my 80D or 650D. I tried another 17-55 f/2.8 when i got my 80D but it wasnt a good experience as far as AF went (never had issues in the past with the 17-55 on my 40D/60D). when i got the 18-135 STM (before getting the Nano) i really couldn't see any difference in sharpness between the 17-55 and the 18-135, at least, not without wanting to see it, and the current verison of IS is much better than the old noisy 17-55 version.
The 15-85 is a good lens, i replaced my old 17-55 with it, but im not sure its that much better than the current STM lenses. It has a good rep though and is wider.
I have a few L lenses, the 24-70 f/2.8mkii included, but i find the 18-135 just works so well unless i need wider or faster. you could get the 10-18 and 18-135 for less than the cost of the 17-55, and have a much more versatile focal range.