I had a DRZ400S, KLR650 set up for adventure touring, and now the KLX250S. Being able to set the GPS on shortest distance and just following it wherever it points is awesome! I have crossed rivers, condemed bridges, rode between a farmers house and barn and explored many many miles of dirt roads and trails. I crossed the Cherohala skyway entirely on dirt. I would love to do the TransAmericanTrail, but I think my time has passed for that big an adventure because my body just doesn't bounce back like it used to.
Sure, you can take the concours down a washboard dirt road, but why put it through that and have to live with the squeaks and creaks that will be permanently with you have the abuse. You can get a used fully set up for touring KLR650 for $4000. If you can't live without the power, you can opt for a super tenere, or GS, or Tiger.
My Versys makes a great backroads adventure bike but isn't going to handle trails and drops very well.