My short answer is to buy the bike you like more. Seriously, they're both real good bikes and you can't really go wrong with either.
The KLR will be better on the highway. The 250 will probably be much more fun on tight twisty roads. Probably pretty even on mild dirt roads where the KLR's weight won't be much of a penalty and the KLX's tires may or may not. I'm not sure the exact range, but would guess the KLR gets over 250 miles whereas the KLX doesn't get much past 100 miles. Much more aftermarket for the KLR. Really, the KLR is a true "adventure bike" - good range, can handle a variety of terrain, but certainly isn't dirt bike. The KLX in is closer to a dirt bike, but with the SM setup, it really is a backroad burner.
Personally, I would get the KLX for the fun factor and the lighter weight, but I'm only 5'8". They also make a kit to bump it out to 351cc. But the KLR is probably the more versatile bike. It probably will be easier to sell if and when you decide you want to get a different bike.
But really, if both have been taken care of, you can't really go wrong.