I'd venture to say that if two opponents had equivalent knowledge of their weapon and the strategies involved in their use, that victory would boil down to specific encounter experience, weapon quality, and luck.
I've witnessed someone with a katana beat a gim, and vise-versa.
I've witnessed someone with a rapier beat a broadsword, and vise-versa.
There are no superior styles, only superior warriors.
It's always interesting to note big-name matches in history and base an opinion of superiority on that outcome, but what about the masters who avoid that spotlight? Odds are there's somebody out there that can beat the "best" that nobody has ever heard of.
As for the european swordstyles, you have to remember that even though a lot of that knowledge was lost or modified for sport when swords left the battlefield, there were hundreds of schools dedicated to the art of fencing at that time and fighters who were masters in every sense of the word. Some of this knowledge was recorded by the instructors of that period, and there is currently a massive surge in interest in rediscovering these techniques through study of these manuscripts and also experimentation.
I've found that most people have a poor image of european-based fighting systems due primarily to the misrepresentations found in popular media, most of which is completely inaccurate, ie edge to edge fighting, improper distance and movement, using piercing rapiers as cut and thrust weapons, etc.
So the question really isn't that simple or fair and is bound to be answered with some amount of bias.
My personal preferences include both the dao and the katana, and I tend to use my katana with a blend of both chinese, japanese, and european flavors. It doesn't mean that my way is better, that's just what works for me.
Interesting discussion guys. Good to see this forum has recovered after that crash a while back