I rode a dual-sport converted XR650R from Texas to Yaviza Panama and back, including hitting lots of jeep trails throughout Central America. Total riding time 250 hours. I have also put 250 hours on a DRZ400 mostly riding trails in the northeastern U.S.
The power on the XR650R is quite mild and controllable, so I don't think that the power per se is likely to be a problem. You didn't say where you are riding, but judging by the bikes you are considering, I am guessing you will be doing a fair amount of off-road/jeep trails. I don't know how tall your girlfriend is or how many push-ups she can do, but I would hope she is above average height and strength or she may find the size of the XR650R tough to handle.
Both bikes have excellent suspension for rocky trails. The DRZ is a bit top-heavy and not as maneuverable as one would expect, the XRR is not so top-heavy but it is heavier, so I am not sure which bike wins out there. The XRR is more comfortable power and gearing wise on the road, although wind blast becomes an issue if you are cruising over 125 kph.
The DRZ has some vulnerability issues, be sure to get guards for the magnesium engine side covers, radiators, and hoses.
My XRR held up very well to the challenge, although the original chain and sprockets were wasted by the end of the trip.
Hope that helps -