I have an 08 KLR 650 that I am happy with after several mods. It has better wind protection than the older pre-08 models and also better brakes, and wider, more sturdy, front forks. From what I have read, the KLR650 is street oriented and the DR650 is dirt oriented.
The stock KLR front and rear suspension is pathetic on any model and will need to be changed out if you want a decent bike. That and a stainless steel front brake line will really improve the handling and braking, so much it will seem like a different bike. Replacing the enormous front fender with a more aerodynamic one helps also. The rest are just comfort, protection, and performance mods.
Its a fun bike and I would take it on long trips except for one thing, crosswinds. I am so used to casually cruising through even the severest crosswinds in my Rocket that I have been spoiled. I just don't want to work that hard, so the KLR stays close to home and the Rocket does the touring.