The new STM version has better image quality and has the STM focus for video which is a bonus even if you don't use it. It is best value if bought together as a kit lens with a DSLR body but if you find a good price it might be a nice upgrade.

You can compare them with the lens comparison tool on this site.

The EF-S 15-85mm is a fantastic lens in both image quality and focal length range (the 3mm on the wide end might not sound like much but makes a big difference) but as mentioned it is a bit more expensive.