My recommendation is to go with the DR for reasons that are based on my observations and formed opinions after studying what type of thumper to buy back in 2002.
One: You don't have to fool with changing out the radiator fluid since the DR is air/oil cooled. If you're racking up the miles, that will be a welcomed advantage during services.
Two: As a previous poster wrote, the DR is more dirt friendly than the KLR which means you have a greater degree of adaptability. The DR's stanchions and tubes will be better right off the lot in the dirt than the KLR suspenders. With some mild spring upgrades, the DR can have excellent suspension. With the KLR, you can only do so much before needing to simply buy a whole new fork.
Three: Although the DR will/might require a seat upgrade if you intend to log some long distance rides, once you do that, you'll have an exponentially more capable bike, IMO. While the KLR's seat is better off the lot, for me that's not a significant advantage. The suspension, motor, wheels, brakes, wiring loom and geometry are far more important to me than those items (brake pads, tires, grips, headlights, seat, etc) that daily riders routinely swap out. For context, how many guys here upgrade their OEM tires on their 4x4 truck as soon as they buy it? Countless dozens, right? I view seats the same way. IF, and I intentionally capitolize IF, the seat is entirely uncomfortable, an upholsterer can do a lot to remedy the problem. I think an OEM seat is hardly a good reason to choose one bike over another.
Four: I don't think KLRs have much advantage over DRs in terms of aftermarket support. Maybe they have more doo-dads but I did a lot of research on DS thumpers before buying my third one back in 2002 and the quality of aftermarket parts for the DR was much higher since many were trickle-down race technology. The KLR will need a slew of upgrades before you even start thinking about hanging race-driven technology on a KLR.
Five: If international travel is on the horizon, Suzuki is a more prominent brand in Central and South America. Not sure about Africa, Asia or Australia.
Six: If you want cheap, KLR will win every time. They have a loyal following because, IMO, they are an entry level bike, there are abundant doo dads to hang on them which gives novice riders a chance to feel like their right there in the race paddock dialing in their bike for the next plateau of performance. For me, hanging a bunch of doo dads on a bike maketh not one a mechanic.
While I'm critical of the KLR, it's a decent bike and there's no arguing that people have ridden them long distances without problems. In the end, you have to evaluate what's important to you, what do you anticipate will be important in your future and what you're willing to pay out to get the bike kitted out to perform the way you desire.
Best of luck with your decision.