Biggest issue: The two bikes handles VERY differently.
Honda 600RR
- has a plastic tank so magnetic tank bags won't work
- actual seat height is lower than 636
- the thinner seat also give u a sore ass quickly
- less storage space
- slightly more forgiving ergonomic so the body/hand/wrist/back sorness kick in later
- more intuitive and easier to read gauge & a fuel level indicator (my personal opinion)
Kawasaki 636:
- more power in lower rpm (don't know about higher rpm comparison since I never got to test the top speed in Honda RR)
- better throttle response with the extra 36cc
- horrible seat ergonomic (the seat is slanted downward so you'll have to get use to supporting yourself with your leg or suffer from painful nut crushing moments)
- you'll get sore & tire must more easily
- MUCH more expensive to insure
Overall, I think the Honda is a better bike for street riding because of the lower seat and more forgiving ergonomic as well as being cheaper to insure. On the other hand, I'd go with 636 if you want a bit more power and is considering tons of twisty/track riding.