The portrayal of Sparta and Athens as complete opposites masks the fact that neither city was one-dimensional.
In Athens there had always been a faction leaning towards oligarchy, the prime example of which being Kimon son of Miltiades, who even had his son named Lacedaemonian. Please bear in mind that Kimon, despite his pro-Spartan views, was in no way in the minority. He was voted to the office of general in consecutive years until about 464 BC by the democratic Athenian Assembly, which clearly indicates that he had the support of the majority of the demos. (The office of general was one of the few offices not allocated by lottery in the Athenian democracy). You need to be aware that in the eyes of the Athenians themselves, the birth of democracy in Athens owed a great deal to Sparta, as it had been with the help of a Spartan army that the Athenians had expelled the tyrant Hippias son of Peisistratus. Athenian democracy was not perceived by Athenians as the undisputedly preferred way of government. When it started it was a completely new experiment no one really knew how it could turn out.
Among the aristocrats it was Themistocles who first realized that – despite its flaws – democracy could confer a unique military advantage, as it permitted the operation of a sizeable naval fleet on top of the standing army of hoplite infantry. As the Athenian empire was built on the foundations of its mighty fleet of triremes, the numerous but poor democratic rowers were able to extract more and more political power from the aristocrats, which shifted the balance in their favour, particularly in the years after Pericles’ death. It is important to realize that during the Peloponnesian War it was the poor rowers who pressed for aggression in the hope of military pay and/or conquests. In contrast, those more inclined towards peace were the wealthy landowners who suffered from the Spartan incursions in the Athenian country side and had to carry also the financial burden of military operations. In the eyes of many, the demise of Athens was in large part due to the flaws of overly unbounded democracy.
In Sparta, despite the thoroughly militarized regime, the constitution had important democratic elements, most notably the Apella. Those with political rights were perfectly equal, as indicated also by their name “homoioi” (meaning "identical") and they amounted to about 9,000 at the time of the Persian Wars. It is true that the Spartan state was less liberal than Athens, but still within Sparta there were differing views. The regent Pausanias is likely to have been a proponent of political change, involving more rights for helots (see also this stack exchange question). At the outbreak of the Peloponnesian War the Spartans are clearly depicted as being divided between the peace-seeking, conservative faction led by King Archidamus – a personal friend of Pericles – and the war-like faction of the ephors.
In the eyes of the Athenians and Greeks in general, the Spartans were regarded as enemies of tyranny and proponents of self-government by land-owning hoplite citizens. Throughout the Greek world this was a very natural aspiration, it was the norm. It was the advent of democracy that first called this into question. The answer could not have been unanimous, not even in Athens.