There are very few diferences other then the 37cc's. The RR also has a slipper clutch, which is great on the track, but not needed on the street. Even on the track 75% of us probobly would not ride hard enough to notice a difference. (slipper clutch prevents rear wheel hop under hard braking)
the RR also has an adjustable swingarm pivot, in this case, 99.99999% of us would ever know the difference if between the adjustments.
Both those features are there for the professional racers, not us on the street, or even track days..
The 6RR is more expensive for a couple reasons, its limited production, and has those extra features.
As for insurance, it depends on the company, call around and see if the 636 would put you in a different bracket or not.
The RR is not as fast as the 636 in stock form, but it was never intended to be. The RR was made for the track, and has a race kit available which makes it a good deal quicker. You most likely won't be able to find a race kit though, all the race teams picked those up quickly..
I don't know the quarter mile times offhand, but they are within a couple tenths of a second of eachother. The 636 is the quickest of any 03 600 class bike.