Long sword VS Katana

i will reiterate a point i made previously. a knight would in almost every case have a shield which would protect him thoroughly if not utterly from arrows IF they were able to "hit their mark" at all
my "hit their mark" has NOTHING to do with the samurai's ability to shoot. it has to do with the arrows ability to pierce the armor. which from my knowledge of Japanese arrow heads used in combat would be minimal at best.
also one can not compare the arrows used for hunting to the arrows used for WAR. its like comparing apples and monkeys.
also the technique for volleying arrows in an arc up and over into the enemies forces was NOT to improve their penetration by increased impact velocity. it was to increase the range at which the arrow would fly. which on a flat pitch would be a 45 degree angle. same technique used for artillery and by snipers. they aim a little bit above their target to increase the range at which their bullet will travel while maintaining killing velocity. however to ensure continued accuracy they counter adjust their scope to take the raised angle of the barrel into account. the killing power of the European arrow was its needle like head which applied the impact velocity into a VERY small space. and the fact that there would be dozens if not hundreds of archers all firing in unison in repeated volleys. so if the first arrow didn't get you the next hundred or so would.

the Japanese samurai used a more traditional shaped arrow head in the early feudal period. and by the late feudal era approximately 1600 (the battle of sekigehara) the arrows were VERY broad headed as i said intended to rend exposed flesh (of which on a knight there wouldn't be any) and as i said cut the cord which held the samurai armor together. also by this time samurai had swayed away from the bow as their primary weapon in favor of the sword. and most battles even in open field melee combat would be more along the lines of MANY one on one duels going on at the same time. and the victor would move on to the next opponent. where as the European style as i said was more like an armored and armed bar brawl. so charlie YES a samurai WOULD very likely agree to single honor combat without a bow. and even if he didn't he would be very unlikely to pierce the knights armor with his arrows (regardless of his personal accuracy and ability) which i will admit would be superb even in comparison to an English archer.. again because of diffrent techniques and different weapons specifically engineered for said diffrent techniques. moreover IF a samurai were able to pierce a knights armor plate.. his chain and leather and woolen padding underneath the plate would mitigate if not negate anything the arrow could do.

now moving away from the bow/arrow back to To sword

the Japanese katana would be hard pressed to be able to breach European plate armor and absolutely would not breach chain. and IF in the miraculous chance it did.. it would be through brute force alone (not what samurai focused on) and would most assuredly ruin the katana's edge. where as a European knight focused BOTH on brute force AND skill. and which skills were evolved around breaching/bypassing a plate&chain armored opponent. where as the samurai sword skills were for fighting an unarmored opponent or one armored in leather and MAYBE wood.

weapon + inferior armor + skill
V
Superior armor + 2 weapons (sword & shield) + strength + skill

i would put my money on the knight

Yet those stupid, armored and shielded French knights and men-at-arms who dismounted and slogged uphill in the mud at two different battles (slow learners) dropped like flies from nothing but longbow fire. 

Crecy
Agincourt

almost exactly a generation apart.  Also see Poitiers in 1356 for the proper time to be dismounted.

in the interest of consitency & control im removing "terrain" as a factor.. its a flat pitched field... for my comments, statements, suppositions, examples

You cant remove terrain as a factor...history used it!!

both european knights and samurai fought battles on flat pitched fields. so there.

my purpose of "removing it" ... using a flat pitched field was such that NEITHER the samurai nor the knight would have "the high ground" so to speak