Well, the Spartans were warriors from birth, fighting was in their blood. I'm sure we also remember the 300, so obviously their tough.
Knights were also chosen to be warriors due to their capabilities. They were highly trained and spent an equal amount of time practicing pretty much. However, in such a battle, it would come down to who could do the most damage to the enemy without receiving much in return.
The Spartans did use some great techniques, but other than their shields, they didn't have much protection when compared to a Knight. In a one on one battle, the obvious winner would be the knight. In a large scale battle, one has to take in all the weapons that were able to be used. For example, catapults would destroy the Spartans phalanx, rendering their greatest advantage useless. In closer combat, the Knights would be able to beat on their shields like drums using maces and such. Also, if crossbows are considered, then the battle is over before it begins.
Keep in mind that a spear isn't going to do much damage against a full set of armor. If a Knight merely jumped on a Spartan, they be crushed...of course, the Knight wouldn't be able to get back up either, but at least the line is now broken. xd
Honestly, I think the Spartans would be toast...mobility doesn't beat strength. I know we all think that the big, tough guy can be taken down if someone just moves fast enough...I'm here to tell you that the fastest ninja who ever lived isn't able to defeat a burly Viking no matter how hard you wish for it. In the end, all the Viking has to do is get a hold of them and it's over. Same with Spartans; once a Knight comes knocking, the game is over.
