the spartans were just better. period.
they were drafted into the army when they were 7 years old, then they had to fend for them selves (steel food clothes etc to toughen them up) fighting is all the spartans know, it is there entire life. the spartans are by far the best soldiers in history! and these 300 hundred spartans happen to be leonidas personal guard, which means that they were the very best of the spartans.
romans can join the army when they are 18 (11 years behind the spartans) and they are well trained but they are no were near as dedicated as the spartans. legionaires had a life outside the army. the romans won wars because of there numbers tactics and tech. but if you take that away and put 300 romans against the spartans they get slaughtered. what superior tech would a legionaire have that would help him in close combat? to make it more even it would have to be the praetorian guard. they are the emperors personal guard and are the best roman soldiers, but even then the spartans are to dedicated and much better trained. plus they have more exp.