Interestingly, my son-in-law and I just made that decision and recently bought dual sports.
He ended up buying a 2007 Honda XR 650 and I bought a 2005 Suzuki DR 650, both off of Craigs List. He paid $3800 for his...I paid $2700 for mine. Both had less than 6000 miles on them. We both initially considered the KLR 650, but after reading about all the problems guys have with them on the forums, we removed them from our consideration. Here's beta on the two bikes:
Honda XR 650- His bike was already very well equipped for off road riding (answers some of the price difference). Additional equipment included: new knobbies, FMF performance exhaust/headers, skid plate, extended range fuel tank, Bark Buster hand guards, reduced gearing and a few other small improvements that most XR 650 owners make to the bike. It is a VERY tall bike. My son-in-law is 6'8" and can just barely flat foot the bike.
Suzuki DR 650- My bike was basically stock, with upgraded gel seat, aluminum billet tail rack, new battery and new street tires. The DR is really set up pretty well from the factory for off road use, but I've added the following to make it more trail ready: skid plate, Bark Buster hand guards, engine guards, upgraded handlebars (stockers are very flimsy- DAMHIK), IMS 4.9 gal fuel tank (in natural color so you can see the fuel level) and new knobbies. I've also swapped out the stock 15T front gear for a 14T. This gives the bike more low end grunt and reduces first gear so it's better for trail crawling.
The bike is still in my shop as I finish the equipment installs, but I'll post a picture in the next couple of days.
One other thought. As you get into dual sport riding, buy the right gear. Right after we got our bikes, my son-in-law wanted to ride a local dual sport route over the Cascades called the Naches Trail. The trail has two routes, one is a logging road the other is a 4X4 trail. Both close in the winter, so we didn't have a lot of time to ride it this season. I was hesitant to go since I didn't have my bike set up for trails yet, but we decided if we stayed on the logging road, I wouldn't have any problems. Well, all was fine until we took a wrong turn and ended up on the 4X4 route. Nothing but mud, ruts, tree roots and standing water...working uphill through the Cascade pass. As you can imagine, my street tires were something less than WORTHLESS in these conditions. I made it, but did drop the bike a couple of times. Not a big deal for the bike as it's built to take it, but I was wearing my street touring boots at the time and I now understand why off road boots are built so much heavier. On one of the drops, I was unable to get my foot out from under the bike because of the terrain and the bike came down on my foot. It didn't break anything, but suffice it to say I was hobbling around for a couple of weeks with a VERY sore foot. I'm now the proud owner of a nice pair of Alpinstar Tech 3 off road boots (did I mention getting into dual sport riding is a great excuse for some cool new gear).
Good luck with your decision!