I pretty much agree with the OP. If you were to throw a ninja in a battle up against a Spartan one on one, he may be able to do some flashy things to catch the spartan off guard, but ultimately the Spartan is just better equipped for a battle. I think much of it also depends on how either one of them could outsmart each other.
For instance I think the ninja would be better trained to know how to set up a trap for the spartan if the ninja was given the time, whereas it would be difficult for a spartan to setup a trap for a ninja. The ninja is trained to assassinate its opponent, and would not subject himself into a wide open battle. He would lure the spartan into a trap and then somehow disarm him, then disorient, then kill.
In the show they depicted the two just meeting each other randomly. In this case the Ninja would not have time to prepare, and if he could not run away he would likely be killed by the spartan. In real life I would imagine the Ninja would run away since he would realize he is not equipped to kill such a soldier.
