For a few years, everybody I knew with a 400S carried on about what a terrible street bike it was. they had all bought the S to use as a dirt bike, but wanted street legality for events that required it. Then a couple of buddies took them to Mexico, on a Copper Canyon trip where a lot of guys were riding 650s, KLRs and DRs both. The guys on DRZs were really tickled with their choice of ride.
Bear in mind that this was Mexico. The longest highway day was 130 miles. Most of the riding was steep, extremely difficult roads. I still don't know anybody who likes the DRZ for highway riding in the U.S.
The KLR is a totally different animal, a street bike that has some off-road capability. It's ok on long highway trips, and in its element on back roads, paved roads, 2-track, in short, on anything you can call a road. I know guys who will ride them on tight single track, but not me. I'll take my DR650 into much tighter places than I will take the KLR.
The changes to the KLR in '08 make it even more a street bike, and less suitable for off-roading. What it has going for it are a big gas tank, a pretty fair off-road capability, a lot of available accessories, and enough room to carry luggage with camping gear. It's a bike that you can ride 1400 miles to utah, then take off the bags and go out and bang around in the desert for a few days before loading up and riding home.
The bikes are different enough that a lot of riders, myself included, find room for both in their garage (my DRZ is a plated E model).
If you are set on one of these two, then the KLR would probably suit you better. For a bike that bridges the gap a bit, consider the DR650. It needs a better seat and a bigger tank (money you would probably spend on the others, too, as the KLR needs radiator protection). It is every bit as good as the KLR on the highway (weather protection excluded), and much better off-road.