Yamaha R1 is a 1000cc machine.
Yamaha R6 is a 600cc machine.
Both are designed for the track hence the 'R' the R6 is lighter but the R1 is a total different kettle of fish the torque and sheer power is not for the in experienced or faint hearted both are fast bikes and are pure sport bikes and are way more than enough for the day to day riding and road. For cheapest insurance is the 600cc which will be perfectly fine and more than the average rider will use in all riding.
Ignore Lord_Darkclaw the R1's came out in 1998 not 1999 and only had 2 colours which was blue and red and white, the blue was far more common but now the red and white is more rare to pick up. This bike blew away all the other 1000's like fireblades. Also the majority of the earlier carb models have been thrashed you will pay between 2,000-4,000 for that age bike R1.
R6 came out in 1999 and was a competition against the ninja, fireblade, gixxer and a hell of a bike.
The new bikes of these 2 are very similiar within looks but power and torque is a no brainer that the 1000 will always win, the new R6's is almost as quick as a early R1 but more tame.
R1 top speed is restricted to 186mph but can get round with power commander dyno jetting race can etc etc which then will do about 190 odd.
R6 top speed is around 165mph but the new ones have clocked 170 odd mph.
For your first real taster of a sportsbike I recommend the R6 and still be careful with it and get earlier model pay around 2,500 for it enjoy it then when you're ready go up the next step and get the R1.
All the best and safe riding!
There is a time and a place to speed.
