For one, its military system is just not that great compared Spartan, Macedonian, Persian, and Roman models of professional or at least trained armies; Greek soldiers generally rejected the concept of military discipline, and in democracies, would hold commanders to account for 'abuses' on campaign. Athens had a large population to draw on, but it would need major reforms to make the most of it.
I would go strongly against the idea that the Spartan model is in any way something to be immitated. Yes they made splendid hoplites but a terrible coast: they had pretty much no commerce to speak off and their economy was completely dependant on the Hilotes, forcing them to spend their down keeping down a population six time their size who hated their guts. In fact, such was their fear of the Hilotes that they where supremely and famously hesitant to even use their army outside of the Peloponese.
Their over specialisation also pretty much made them ditz in all other aspects of warfare such as siegecraft, naval warfare (the fleets where supplied by revolted athenian allies during the last phase of the Peloponesian war and strategy, appart from the od ones like Brasidas and Lysander.
Finally, they where also extremely vulnerable to even small looses among their Homoios population (the actual spartan citizens and the hoplites who made the legend, the rest of their army was average, including the Periocois). Athens could have easily srughed off, and did, a defeat like the ones Sparta suffered at Sphacteria with 500 hoplites captured. For Sparta, however, it almost destroyed her and had she not been lucky at Mantinea it might very well have. When she was facing with an actual large scale disaster in the aftermath of Leuctra she was done for as a power of significance in Greece. Athens, on the other hand, was able to take similar blows four or five time before being truly K.O.
Sparta was lucky on an almust painfully ridiculous level during the Peloponesian war. She had the plague, the Argives snatching defeat from the jaws of victory at Mantinea, the Sicily expedition, Alcibiades pretty much spelling out to them out to win to supply for their lack of strategic intelligence and the Persian and the revolted athenian allies making most of the job for them. Getting even one of these factors out could have changed the outcome drastically. Having things being more balanced would have resulted in Athens breaking Sparta piece by piece.
As for the greater pictures, I believe its usefull to note that Golden Age Athens actually fought Persia one on one and was winning, solidly, and that even with the plague Persia didn't dare trying to take advantage of the war, such was its fear-respect for Athens possibility and that she needed the Sicily expedition for that.