hey guys im working on my degree in history with my major in military strategy, and agree that the spartan would most likely win most of the time. There would be times where the ninja would win but there would be a higher chance for the spartan. they were trained to fight both formal enemies and more importantly the eastern armies of the Persian states who had gear very similar to the ninjas of japan. they both wore light cloth and leather armor, both had the same basic weapons(short sword, daggar, bows, and throwing weapons) and the spartans knew how to fight against those weapons already. also, the spartans had some of the best fighting methods at the time, they wore very light if any armor, helmets had a very lerge firld of view but could deflect direct hits from an arrow. thier shields were used as both a offencive and defencive weapon. they also wielded a spear and heavy short sword(weighing up to 2.5 kilos).
The bigest thing though is how they fight, spartans have trained extensively to fight easter style warriors while the ninjas had no experience with western style fighting which is a very agressive block/counter style.