If ya are stuck on these two the 650 is a better dual sport because the close ratio gearbox of the DRZ allows it to either be a dirt bike or a street bike depending on sprockets. They both make about the same 35hp stock, weigh within 20 pounds of each other but the DR is lower which is nice on the street and not a big deal off-road because ya aren't gonna be jumping or really burning on either. There are much better street bikes, dirt bikes and dual sports out there but a DR650 will do the interstates and off road exploring without much drama. If ya want more power, less weight and better handling. KTM/Husky/Berg... have it.
I've forgot more than you kids ever knew!
Retired and living off the interest on the money I owe.