I'm sorry that this didn't get responses. If you're interested, a former Athenian general named Thucydides actually wrote an account of the History of the Peloponnesian War during it (he died a bit before it ended, leaving the history unfinished), the Peloponnesian War being the one between Athens and its allies and Sparta and its allies. So I can pull that up tomorrow and give you some specific examples of battles. Basically originally the Spartans were the best at hoplite battles, but there were only a few thousand spartans total (as in the full hoplites/citizens, Sparta the city had more residents but there were only around 8000 spartiates. (They also fought with slaves and other Lacedaemonian allies though, Herodotus mentions that in the war against the invading Persians they marched to battle with 7 helot (slave) soldiers for every one Spartan. At this time the Spartans were confidant in being able to beat any other Greek soldiers, and though at the battle of Plataea they ended up fighting Persians and not Greeks, they and the Athenians completely routed a much larger invasion force.)

The Athenians were known for having absolute naval supremacy, and bested the Spartans at the Battle of Sphacteria (425 BCE), where they were basically able to pin down the Spartan hoplites on an island and continually shoot arrows at them until, for the first time ever, they surrendered, and the Athenians brought back over a hundred Spartan prisoners to Athens. This completely changed the war, as the rest of Sparta were unwilling to attack any more or the Athenians would execute their prisoners.

In the end, despite Athenian naval supremacy at the start, the Spartans under Lysander completely crushed the Athenian fleet at the battle of Aegospotami (405 BCE), ending the Athenian empire. So, Spartans are looking pretty good.

But, in 371 at the Battle of Leuctra, the Thebans (who had been allied with the Persians a hundred years before) finally crushed the Spartan army in a straight up fight. Xenophon, another Athenian historian, is a good source for this. And this battle totally ended Spartan supremacy, and they basically stopped being such a prominent city ever again, and later they lost another battle to Alexander the Great's forces under Antipater which hugely thinned out their numbers.

So, for Spartans evenly matched and then winning, check out Thucydides, for their defeat check out Xenophon. I can try to find citations to specific battle scenes tomorrow.