Knight vs Samurai, interesting, but first, I'm going to derail a few common mistakes concerning the european knight.
The suits worn by knights were neither bulky, nor as heavy as they said to be in most text books and the like.
This is a common misconception, due to the fact that nearly all serviceable suits of plate armor were destroyed through the ages, as they were used and eventually fell apart due to little upkeep, rotting away from moisture, and the like. Most of the suits we have on display anymore, are decorative suits, which were made for show and nothing else.
The average knight could have been knocked off of his horse and gained his footing again without major difficulty. Infact, using the various recipies that were left over and styles, from the era, there have been models of the armor made, which allowed the wearer to mount a horse on their own or even do a cartwheel, without major hinderance.
Why would someone wear something that would make them helpless? Mobility is much more important in combat than being able to shrug off one or two hits.
Can Knights get up after they have fallen?
A knight in armor for battle was very mobile. If he wasn't, he would be susceptible to attacks from behind or from a faster moving unarmored opponent. In fact it is recorded that some knights were able to leap into there saddles from a standing position beside there horse. It is completely untrue that an armored man was unable to get up after falling. The old story about a knight being winched up in a crane to get on his horse is a figment of Mark Twains imagination i.e. "Connecticut Yankee in King Arthur's Court".
http://www.armor.com/2000/info.html
BUT...
The samurai has the lighter armour and the european knight, even on horseback, has the problem, that he can't move as quickly. His suit is heavier than the samurai armour, thus he gets worn out faster than his opponent, who's also more used to fight on foot. The samurai has learned to master the sword, which is the best melee weapon on earth. It is superior to ANY european sword (some of them were made of 100,000 layers of steel). It can cut through basically any armour (except Mithril :P ) as long as you have the right force behind the blow.
Summarizing it has to be said that the samurai will most likely win. He is trained to fight with only a sword and has no shield, he knows how to move quickly, how to avoid strikes, how to strike back swiftly. The european knight has his strong armour, but that wouldn't help him much on the long term, in fact I'd say it would be a disadvantage (when you look at the 100 years war in france it's clearly visible that the heavy armoured knights had their disadvantages, especially against ranged attacks. Now imagine samurai archers with english longbows... scary thought).
Besides the fighting styles are extremly different. And while the samurai has a philosophy behind his training (I never managed to find anything similar to Bushido in europe), the european knight is basically a barbarian who just goes around smacking his enemies with his, poorly crafted (compared to master-made katanas) sword or flail.
The knight's main purpose on the battlefield in the ending Middle Ages was simple. He was the "tank", his job was to go into a charge with many other heavily armed riders to break through infantry lines. But that disappeared quickly once the ranged weapons turned out to be more accurate than ever before (english longbow, steel crossbows and later... firearms). In the end, the knights stopped being heavy cavalry and even cavalry made up of commoners didn't last long. Cavalry quickly turned into something new. They dropped the armour and became more mobile and faster.
On the other hand the samurai is a highly skilled swordman, there is no equivalent on the european battlefield. Even samurai cavalry was light and the samurai has the advantage of mobility.
Besides, the samurai armour is cooler and the swords just kick ass (they're extremly well balanced and a dream for any swordfighter... *looks forward to see the family sword*) :twisted:
As for the length of the fight, well... Looking at how quickly points are scored in kendo (those are the times when I make my GF giggle like insane, cause I often don't see the hit) I'd say a real fight would be short. Fights lasting minutes is... Hollywood fiction.
Interesting would be a fight on horse back. But I'd say there the european knight clearly loses. He can't control the horse properly, his stirrups are too long and the saddle not made for accurate dressage. Sure he has the lance, but he has to hit with that first, and that's not easy. I tried it with a german WW2 lance and that was nearly impossible in the beginning. I'm quite good now. But I have to say, I think even I would be able to defeat a european knight on horseback. I'd be more mobile, I would be able to control the horse better, I can make moves with it (moves based on the renaissance cavalry which are still in use in modern equestrian and in classical formations like the Spanish Riding School in Vienna or the Cadre Noire in Saumur) which the knight wouldn't be able to counter. And if everything fails, I can always outrun him (and turn around and blast him with a rifle :P ), since my modern-bred horse would be lighter, better trained and more agile than his huge warhorse (same goes for the japanese warhorse. They were light and agile)
We also must not forget to consider the height of the 2 fighters. The european knight would be way taller than the samurai, which is, in martial arts, usually a disadvantage. The smaller one might not be as strong as the opponent, but that doesn't matter a lot. The smaller one can move faster, dodge and duck more quickly, etc, to make it short, he'd be more mobile. And mobility wins wars.
Anyway, I'd say in ~70 out of 100 duels the samurai would win. My GF says that it would be more like 99 out 100, but I think that's a bit too much (not to mention she's biased *blames her samurai ancestors*). Ok, I gotta run before I get smacked with her shinai... *RUNS!*