Can you picture this if it came down to fighting alone?
Snake Eyes, employing his ninja skills with a Katana going at the greatest warrior Spartan of all, charging him with shield and spear, sword and fists?
This is one heck of a close match up. Gear, style, ability are all almost even. Almost. Look goes Snake Eyes all the way though.
Even so, does Achilles have the means to defeat a ninja and a warrior trained in every combat form known to man up to the 21st Century?
Then consider this: in the midst of the fight, as Achilles comes at Snake Eyes to meet blade to blade. Snake Eyes pulls the Uzi.
Winner: Snake Eyes