Honestly, after reading everything here, I'm leaning more towards the katana user, if for no other reason, because it's so much more versatile.
There are some problems in this debate though that people seem to be overlooking a lot here. One is how many people have come in and said, "I don't really know anything about using a katana, but I certainly know about rapiers and I think the rapier user would win." There's a problem with this kind of statement and I think everyone should realize what that is.
Another is that there's a lot of people trying to discredit the katana just because of its fanboyish popularity in some areas.
And one more is that, given that all of us are typing in english, I can assume that most of the people here are people that have grown up in "western" countries. The rapier is a western sword. There are classes based around fencing (And yes, fencing uses just one kind of rapier, I know) in the western world more than there are ones based around the use of a katana.
I guess my point is this. I think a lot of people are overlooking the fact that when you know something far more intimately than another, you're likely going to prefer it more.