The Peloponnesian War pitted Athens and Sparta (the two greatest powers in the Greek world at the time) against one another in an intense military conflict. While this struggle is often presented as one pitting the Athenian fleet (as the naval-based power) against the Spartan army, in some ways, this picture is overly simplistic, given that Athens itself prized military service as a critical component of civic virtue and had a powerful army in its own right.
Meanwhile, the vaunted Spartan army, powerful though it may have been, had been (throughout Sparta's history) primarily used defensively, given how it existed as a tool of suppression against Sparta's helot slaves. In this sense, as powerful as its army might have been, Sparta always had to be careful about how and where it employed it, given that its internal stability depended on its army's continued functionality.
When comparing the two sides, Athens was, by a significant margin, the wealthier of the two, as it was able to draw tremendous wealth from its far-reaching empire. However, much as was the case with Sparta's army, the Athenian empire could be seen, in some respects, as a weakness as well as a strength, given that the possession of empire carried with it the necessity of defending that empire from its enemies: if they could not target Athens, Sparta could still target some of the weaker cities on which Athenian power relied. Additionally, Athens also would have had to contend with insurrections from its subjects.
In some respects, however, especially when seen within the context of the Peloponnesian War, Athens's greatest weakness may have been its democratic system. Keep in mind, Athenian democracy was not a representative system as you see in modern democracies, but was rather a direct democracy, one featuring such political tools as sortition (selecting officials not through election but by random lottery) and ostracism (by which citizens who had grown too influential and powerful could be sent into exile). This system of government was, by its very nature, prone to high levels of instability.
In the earliest part of the war, these drawbacks seemed to have been mitigated by the leadership and influence of Pericles, who provided a coherent picture of what Athenian military strategy should strive for; but after Pericles's death from the Athenian plague, that coherency would disappear. I would suggest that, by looking into the history of the Sicilian Expedition, you might observe a powerful illustration of this particular theme.