I had both, until recently. Had the KLR for 4 years and loved it, but it just wasn't for me on long on road journeys. Off road on nearly all terrains it was almost perfect, logging, forest, mud, even single track it did very well, above my capabilities anyway.
I got the Versys and the KLR never came out of the garage again. V is an excellent commuter, long distance tourer, two up or one with full camping gear, its great in the twisties and you can have fun on logging and forest roads. It will not handle big potholes well (alloy wheels are lightly to bend and let the air out suddenly). Plus the engine and exhausts are very vulnerable.
So decide on your riding preferences and the decision is easy. Both are excellent bikes and you won't be disappointed with either. KLR is rough and ready for anything, Versys is a smooth, great handling pocket rocket.
Only downside on a V, you'll probably pay a bit more insurance, many companies view it as a sport bike, KLR as a dual sport is cheaper to insure.