A rapier is at least not heavier than a longsword, and a longsword typically weighs slightly less to the same weight as a katana, while being significantly longer (on average, of course).Ieyke said:snip
And your argument doesn't make sense about the quillion - the quillion adds the ability to apply torque perpendicularly to the grip, which is not present in the katana. The rapier's grip is also not circular. In fact, I've never encountered any type of sword with a circular grip, because the human hand isn't circular.
The katana may be able to play the rapier's game, but then so can the longsword, which the rapier fencer had to know how to deal with anyway. There are differences in technique between the katana and the longsword, but the longsword is widely considered to be more versatile (two edges, more robust, capable of binding with quillions, etc.).
It is also worth noting that, despite people's perceptions, the rapier can cut, albeit not as well as the longsword, broadsword or katana (or sabre and so on). One simply has to look at rapier according to Swetnam to see that he quite likes the cut with a rapier, and he was using them.
However, I do agree that the more versatile weapon has more opportunities to win. But, as always, it comes down to the skill of the person wielding the weapon, and there is no reason to believe that the samurai should be inherently superior in skill to the rapier fencer.