my 06 636 had a heating problem I could never fix either. I rode that bitch hard as hell though (was my track bike). I personally love 636's, and the 03-04 is sick! (i just picked one up). Only because of personal distaste for the 03-05 r6, I'd say get the 636. but then again if you can't solve the heating issue you're gonna be disappointed in a sick *** bike. So if you like the r6 get it.

 

My R6 is the ****. Spent 50 bucks making a new subframe at Tractor supply and that thing is bullet proof. They are real easy to make but you can also check out Atown customs. They make a sick Subframe for that bike.

Only the older R6's up to 02 have had this problem

 

Go for the R6 i have an 03 and i love it i broke the subframe on it with in like 3 weeks but i replacved it with an Atown sub frame and now that thing is better then most 636's and stronger as far as the tranny prob i have run yamahas forever and never had a problem as long as you know how to shift and change the oil every once in awhile. go for the R^ you know whats wrong with it and it happens to be the only week point on the bike.. It is nice cause it wont stall when your slowwing way down to like 2 MPH on the bar...