I have the Suzuki V-Strom DL-650 which is an "adventure" bike. I chose it for many reasons including legendary reliability.
I was looking at the Yamaha Super Tenere - nice looking bike seems very capable. The KLR is highly regarded as is the Suzuki DR-650S.
Depends on what you're really going to do with it. If you'll spend time in rocky trails and class 3-4 roads - go with the dual sport.
If occasional gravel and dirt roads with some touring you want an adventure bike.