@bugrimmar
That is a classic stereotype you are playing into. I thought I was quite illuminating, and obviously I didn't get the point across as well as I would have liked. Let me make it simple. Spartans didn't just have assassination experience. They were outright assassins themselves. They lived in a society where they had to terrify the peasants every year to keep them in line, and away from launching a full on revolt. So this may come as a revelation to you, but a Spartan would probably not only have more training then a ninja, but a great deal more experience. In the final analysis they would be considered better assassins.
Your assuming that the Ninja would be the aggressor, but here is what you are missing. A single Spartan solider out in the field alone would be out there for the specific purpose of performing assassinations. So all those vulnerabilities you are ascribing to the Spartan solider apply equally to the Ninja. So it is equally likely that the Spartan is the one to come creeping out of the night to murder the Ninja as he sleeps.
This isn't about a clash of styles. Both were adept assassins. The only telling difference is that the Spartans would be the recipient of better bonuses. Better equipment, training, and on the job experience. That means they were probably the better assassins. Further more whether you like it or not. Assassination is not a fool proof method in the first place. The tactic can be thwarted based on the preparedness of the opponent, and as I pointed out early on in this reply. A lone Spartan by default is already in a highly prepared state. He is going to be concealing not only his movements, but being extremely vigilant of his surroundings. He will not be apt to approach any location that would allow him to be easily ambushed, and when he does sleep he will have already seen to a well devised concealment. Any Ninja stalking a Spartan who is by default not following a predictable pattern is equally likely to expose himself.
Anyway the scenario would never actually occur. While a Spartan might choose to engage a Ninja out of a sense of basic blood lust or security. A Ninja would never choose to engage a heavily armed, and armored opponent like a Spartan. The Ninja would opt for avoidance, or if the encounter was unavoidable the Ninja would retreat with all due haste. So the only real question is whether the Spartan would be able to chase the Ninja to ground. I think that is more of a coin toss. The Spartan would be heavier with better conditioning. The Ninja would be much lighter, but would have less stamina. Due to being a contract killer. So it's only a question of who can go fastest in a quarter mile. Which would be the point where the Spartan would simply collapse from exhaustion. So the fight would only end in one of two ways. The Ninja escapes, or the Spartan kills him.