no DxO here. Those are JPGs out of the camera (7D here as well)
As far as barrel distortion goes - u'd probably not be able to identify any difference in the result between 17-85 vs 15-85 after DxO (the 15-85 photo would still be sharper and more contrasty though).
DxO does an INCREDIBLE job in fixing lens distortion. It is so accurate, even in scenarios of complex, non even distortions, that u'll get perfectly lined squares out of each photo. Some lenses, the diff is negligible (for instance my 50mm f/1.8 has so little BD I could not really tell the diff unless I run back-forward between the two), whereas for some (such as the 17-85) it is huge.
if you will look here (again, best seen when copying and going back and forth) - this is from a REALLY old sample of mine (still with DxO 5 and on JPGs, since before I shot RAW, but barrel distortion is very good here)
This is the image straight out of the camera (on the 17-85 @ 17mm) - you can see very noticeable barrel distortion
whereas this is the result after DxO:
if looking closely, you can also see even at this lowly resolution that the original image has a lot of corner CA, while the fixed one has less. If you want I also have a sample corner crop of another photo -
This is the corner (top left) out of the camera with the 17-85. Here you can see a lot of CA and also very soft:
Same corner after DxO (again, DxO 5 on JPG):
So, and this actually can relate to the OP as well - the cheapest possible upgrade to 17-85 is to buy DxO. I got my 17-85 about 4 years ago to replace the 28-135 I used on my old film SLR, and I was hugely disappointed with it from the beginning. When I discovered DxO, and saw what miracle it can do for such problematic lenses, it was a huge revelation. I did not have enough money back then to buy any high IQ lens, plus there weren't really none (the 17-55 only came out later), but the DxO managed to take away a lot of the problems of the 17-85. Naturally, DxO can not add detail so at the end of the day it's still a mediocre lens. But the improvement DxO gave it was, for me at least, the difference between "I really hate this lens" to "I'm ok with this lens and I'll upgrade it one day"
The 15-85 is of course a lot better, in terms of corner softness, CA, etc. The problem it does still have, DxO fixes as well, so it's still a great tool. But the difference between the out-of-the-camera IQ and the post-DxO IQ is smaller than it used to be for the 17-85.