the 6R is 636cc while the R6 is 600cc (or 599cc, whateva)
i would guess the 6R would beat the pants off the 600cc since it can hang w/ GSXR-750's
im not sure how "LIGHT" the R6 is, but i know the 636 weighs 355lbs or so dry...(i remember comparing stats of the bikes last summer when i got my 6RR (600CC), i was pretty sure the kawi's were the LIGHTEST...although i dont see how much the weight effects the bike, if you have a bike that is 5lbs lighter than the next guy, but you weigh 40 more lbs that the guy on the heavier bike, i would guess the weight of the bike is cancelled out!
either way you go, im guessing you will be happy since really you have to ride both of those bikes on a track to really appreciate their power (i had mine up to an indicated 160mph)
unless you are new to riding, in which case you should get something tamer...like a sv650 or ninja 500
i got the kawi last year and loved it, i wanted to get a R6 but there were practically NONE in FL, and once i saw the 6RR in green in person, i fell in love