a spartan - He would be very fit, motivated, high morale and have a lifetime of military training but primarily as a formation fighter not individual warrior. However, his armor would be outdated, his weapons designed for formation fighting and not condusive to individual combat.
a roman legionaire- Very similar to the above.
a japanese samurai- A lifetime trained warrior, skilled, high morale, fights from horseback and skilled at horse archery. A very strong contender but his armor is weak.
a mongol horse rider- Skilled horse archer and combatant almost born in the saddle, tough as nails from a harsh life. Another strong contender.
a crusader- (which crusad) A mounted fighter trained from birth to fight as a warrior, an individual. Heavily armored, mounted, high morale(fanatic Christian). A very strong contender.
a biteme- a harsh life,bitter marriage, fanatical bad poster (high morale) physically fit- but not on the 400m track. raised on the dairy.. looks like james hetfield. highly regarded as possesing powerful 'decapitation' abilities. strong contender.
or a viking?- Tough from a harsh life, fights as a warrior but poorly armored and his weapons are not effective against heavy armor.
Now, it has to go to the mounted warriors, a man on horseback has a distinct advantage. If you allow ranged combat the Samurai or mongol could get a lucky shot and kill or seriously wound the crusader or his horse before he closed. The Samurai beats the unarmored mongol as he is better protected. If it comes to close range the crusader has an advantage due to his heavier armor. Just my .02