Which would be the "better" walkaround lens?

I have had both the 18-135 and 15-85. I take most of my photos on the wide end and I was dissapointed in the image quality of the 18-135 at 18 mm. While it wasn't bad, it wasn't super sharp either. At the 135 mm end it did have very nice image quality. I do miss the lens since I sold it for times when I really wanted to bring only one lens to cover a large focal range. But I really wasn't using it much since I bought the 15-85. I notice a much bigger difference between 15 and 18 mm than I notice between 85 and 135, but it just depends on what you shoot.

If you look at my Utah and Colorado photos from 2010 in my gallery link in my signature, those are all shot with the 18-135. All my photos from Utah and Colorado 2012, Yellowstone, and Glacier are with the 15-85 mm(except for a few wildlife ones that are witht he 55-250) if that helps. Practically all the photos in my gallery are with those two lenses.

"I can't decide which lens is the better compromise for day trips where photography isn't the primary purpose of the trip...the smaller focal range with better IQ or the longer focal range with mediocre IQ/sharpness."

As a day tripper, you cant go wrong with the 15-85. A one body lens set up. I own both the 17-55 and 15-85, and I want to tell you you are not giving up much in IQ with a 15-85

As RPCrowe says, a slick way to travel is with two bodies that use the same lenses. In your case you have a 17-55 and 70-200II , so if you picked up a 30 or 40 body, very reasonable I might add, you have everything coverd at 2.8 . However with that said, it sounds like you want to travel light with one body and lens.

Food for thought !!!

Mornnb: The 15-85 has similar image quality to the 17-55 and 24-105? Apparently, you don't pixel peep.