I have to echo several of the above notes, ground clearance (more would be nice), skid plate (necessary, several good brands), crash bars (necessary, several good brands), rider skill. I too went from a KLR to the Tenere. With the superior power/balance/ride of the Tenere, the difference was like day & night on the same roads and trails. Even with the additional weight, the Tenere is faster & more stable & more capable than my heavily modified KLR ever thought about being.
3 of us a couple years ago did the COBDR, 1 bike had the 804/805 Shinko knobbies, another had the stock tires, & the other one had the Shinko 705's. The only part where 2 of the 3 didn't make it was thru the long deep gravel/sand section outside of Buena Vista. The front end does feel really heavy in the deep sand like mentioned in another post.
We have taken our bikes just about anywhere we took our KLR's. Picking the correct line, watching the speed & knowing that you are on a 600# bike helps keep things in check, most of the time...
The Tenere really opened up the state (CO) and the surrounding areas. Much nicer to ride for 1-2-3 hrs or days to get somewhere to ride, ride off road for a while & then back home. With energy & non body soreness the next day to do it all over again.