In all honesty, the winner would be determined by the environment and duration of the battle. Amazonian tribes practise cannibalism so if the battle became really drawn out, they'd out-sustain the opponent simply by having more food readily available; even killing one or two of their own to feed 10 if need be. On top of that, if the environment of the fight was plant-rich, amazonians are far more knowledgeable about what can be eaten, what can be used as poison, et cetera.

Since probability dictates that the battle would probably not be an all out one where they go all in, the Spartans would slowly lose energy while the amazonians use their superior ability to make use of anything as food to win.

Another thing to consider is that Amazonians regularly use stealth and hunting tactics to outsmart opponents, if the Spartans began splitting up into smaller bands, the amazonians would win because they are very good at smaller battles.

The last point to consider is that Spartans are extremely chauvinistic, only the males above the age of 13 of their population can fight effectively. Amazonians are very egalitarian, the women hunt with the men, the children learn to both catch, kill and cook prey from a young age. There is no one facet of theirs that is fighter-only and one that is sustain-only. No matter who got killed amongst them, they would be better all rounders whereas if the Spartan men began being taken out, then the women would begin to be targeted (only the women of Sparta knew how to cook and such things), Amazonians also know ar more about makeshift medicine with plants, Spartans didn't believe in medicine because the Athenians knew all there was to in that regard and they never saw reason to care.

The final issue is mercy. When it comes to slaughtering an innocent child or the women of the enemy populace, the Spartans would more likely hesitate and welcome them in instead. The women and children of Amazonians would sneakily kill the shit out of them at night. On top of his, Amazonians have no mercy and have been known cannibalize women and children of foreigners very tactically.