Check for clearance on the swingarm, the mud flap in front of the tire, the chain, and the muffler - a friend of mine had a Big Gun exhaust on his KLR that hit the tire when the suspension took big hits. Also, I would guess the KLR has some frame bars under the rear fender, make sure that it or the bolts that bind it to the fender don't touch. You'll hear a horrible grinding noise if they do, and it'll chew the knobbies right off the tire. I had this happen after I installed some longer bolts onto my rear fender to mount some side racks, and didn't have time to cut them down for the weekend's ride.
As for what different tire sizes buy you, a wider tire will give you more traction off road and a taller tire will have the same effect as dropping a tooth on your rear sprocket, though the difference is smaller.
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Wright Bagwell
http://www.geocities.com/wwbagwell/