The 6RR was built to keep inline with AMA racing standards to keep it running in a certain class. The 636, if raced in most organized groups, would have to be classed with the 750cc bikes. For street use, the 636 is a better choice because of the gearing and added torque (though not very much at all). The 6RR is geared more for track use, and for 03-04 models, it came with a slipper clutch, which was not available from the factory on the 636. Kawi did change that for the 05-06 model years, but now for 07 they are no longer making a 636. It was a short lived idea, and I think they(Kawi) weren't so happy with the 636 being labled a cheater bike. The additional 37-38cc's gave the Kawi an advantage over the other 600cc class bikes.
If you are not into racing, then go with the 636 for 06 and prior models. If you plan on racing, then go with the 600. That way you don't get your butt handed to you by the guys on the 750cc bikes. Either bike's are great for track days. Just my 2cent.