The KLR650 is the AK47 of motorcycles. It's simple and reliable as well as hard to break but not flawless. It's heavy and big, the brakes and suspensions could be better, it vibrates (IMHO not as bad as the F650 GS and Dakar I used to own. Could not ride the Beemers around 3500 to 4000RPM without the world turning into a blur).
It's not really fast and it does not like "jeep swallowing bogholes" or bottomless sand pits.

But:
The KLR will handle everything you throw at her. Somehow.
If you don't know exactly what's going to come your way it's your bike.

The DR is similar but a bit more sophisticated in some aspects. It's lighter and the brakes and suspensions work better. Although the size works fine for me (rather skinny and 6'4") as well as for short riders (easily lowered without having to sacrifice too much of the quality of the suspensions) it's not the choice for supersized guys as the seat seems to be off the MX and trail bikes parts shelf.
You will have to get a big tank or a 10 l jerrycan.

I never bothered about a center stand on a DR or KLR. If you reasonably fit you just use two bricks, a log of wood, a tool box, a tree trunk, whatever is at hand. The luxury (or girlie) solution is a Toyota scissor jack from the scrapyard. Weights about the same as an aftermarket centre stand but is more versatile and does not limit your ground clearance :-)