I currently own both.. '05 KLR (15k miles) and Versys (850 miles). The brochure says they both have the same purpose in life (dual-sport/adventure bike). That's quite a stretch....
KLR 650... Rock solid, dependable, cheap and easy to work on, cheap parts, huge aftermarket, huge level of peer support, plenty of power/torque for the majority of riders, plenty of space for passenger or luggage, handles better than you think it would, very roomy cockpit, upright seating, seat is OK, mileage is around 50mpg, excellent range, will go pretty much anywhere a sane person wants to go and back.... fun 'do everything good nothing great' ride
BUT... she's top heavy, long reach to ground, they say it'll do 100 mph but it lacks guts above about 70 mph, 50/50 tires howl on the road, that big thumper vibration (not bad really), 20 year old tech, feels very busy above 60 mph, 5 speed tranny (6th would smooth out the hwy busy-ness, crosswinds aren't fun. low watt output for accs., brakes suck but you get used to them, very heavy for real off-road.. works but will wear you out.
Versys... Put a bag over her head and she's gorgeous..LOL, very smooth and peppy motor, 6 speeds.. effortless 70-80 cruise, modern fuel injection, good wind protection, great lights, upright seating, very nimble, good brakes, 50 mpg, very minor vibration and buzzing issues, peer support is decent and growing,
BUT... the seat... damn the seat, reach to the pegs is a little short if you're getting old and have been on a KLR for the last 15k miles, aftermarket is slim but growing, off-road... no way, graded dirt and gravel... ok if that floats your boat, but after riding the KLR, the Versys suspension is out of its element. Well......... can't think of anything else.
The '08 KLR fixed some of the faults in the earlier model.. better brakes, smoother motor, better wind protection, better forks.
Versys is a much better road bike with great handling, easy to handle power, great lights... sucky seat, and limited off-pavement capability. The KLR is less refined on the road, but is truly capable off-road. If you want to go fast, stop fast, turn fast and don't have any real urge to adventure off the beaten path, the versys is hard to beat. If you want a good all-around bike, and like to get muddy now and again, the KLR is a fine mount.
hope that helps