I had the same problem with my choice as well... was bouncing between the KLR and the wee big time. And to make matters worse I had friends that owned both the newer Klr and the newer wee's. So I test rode both for a day
bad idea. It screwed me up even more. I wanted both in the worse way.
The KLR is definitely more suited for the off-road then the wee (hell it comes ready to go off road without really doing any additional stuff..nor do you have to go in debt getting it ready buying aftermarket skid plates, etc.), just as the wee is all the more about the road. Both can do the other, but you're sacrificing something both routes. Honestly, if I was in your position and lived in your location I'd hit up the KLR, however, the wife wouldn't set foot on the back of it with me EVER. The new 08 doesn't have the vibration that the older models did, and they definitely enhanced a lot of other things about the bike as well. It handles excellent on the road, and far better off road. It is truly a "duel-sport". However, the seating of the bike isn't the best for long juants (easy fix..by the corbin seat for it)...still not the greatest, but better so long as you don't consider putting someone else on the back. The nobby tires are going to be a bit more noisey and noticeable on the road when cornering too. Of course less wind protection too.
While both are tubeless...the Klr is obviously spoked and the strom cast...this scares me a bout my strom when I go to take it off road...break a spoke in the cast wheel and I'm done and have to purchase a whole nother tire, spokes on the klr ...no big deal! Also, as mentioned...you'll have to shell out some cash to get the strom off-road worthy. Plastic cost a lot too...the KLR seems to have less and the stuff it does have seems to be less spendy by far.
Personally, I went with the strom cause I live in maryland..not nearly the amount of off road stuff..plus I only have two other friends that ride off road with their stroms and klrs...so if I'm not with them, I'm probably on the paved stuff. Plus I have a 100 mile commute to work every day on the slab...not a big deal, but I definitely like the wind protection of the wee and it does tend to have a little more juice in the higher speeds then what the Klr does (klr isn't too thrilled with the ride when they try hitting above 80mph to get out of the way of someone, or whatever).
If there is ever a possibility that the trails you are talking about riding on now may get you to the point of wanting to ride something more technical and a bit more rough, then go with the KLR. IMHO (and I'm younger then yourself still seeking the adventure a bit..maybe too much sometimes), if I lived in your area I'd most definitely go with the KLR due to the terrian I know that you have vast amounts of and we're limited here with.