In Athenian democracy, not only did citizens participate in a direct democracy whereby they themselves made the decisions by which they lived, but they also actively served in the institutions that governed them, and so they directly controlled all parts of the political process.
Other political systems
However, not all ancient Greek city-states were using a direct democratic system.
Other city-states had, at one time or another, systems of democracy, notably Argos, Syracuse, Rhodes, and Erythrai. In addition, sometimes even oligarchic systems could involve a high degree of political equality, but the Athenian version, starting from c. 460 BCE and ending c. 320 BCE and involving all male citizens, was certainly the most developed.
So, whether it be a semi direct democracy, a representative democracy, an oligarchy, or dictatorship, how did Athenian democracy compare to other ancient Greek city-states using a different political system in terms of the living standards of the citizens? Were the citizens in other ancient Greek city-states that were not using the Athenian model, worse off, or better off?
Living standards do not depend only on type of government, but on technology development and other factors, like natural resources per capita and economic extraction abilities (taxes).
Certain types of government foster the appearance of new technology, or foreign technology adoption. Democracies are certainly an open type of government that favours technology.
Nonetheless, Ancient Greece had very few resources per capita. The land is dry, and there's not much arable land. That was a major factor in the colonizations: many, many people left Ancient Greece because of the poverty. The majority of the population in Ancient Greece lived just above the subsistence level. As advantage, Athens had (has) quite a large arable hinterland, but not as much as Thebes did, or other cities did, in Macedonia or the Peloponnese.
That said, Classical Athens did have a dominant political relationship (very good terms), to extract taxes on other Greek cities using the Delian league. This was unmatched during Ancient Times in terms of added prosperity to a Greek city. The revenues were huge. Sure, that Athens was a democracy helped organize and maintain the League, but you should consider also simple military factors on this (aka: the unmatched Athenian Navy).
To conclude, the spoils of war is a factor to consider too, because of the difficulty to obtain metals in Ancient times. Athens had access to large amounts of metals thanks to the victories in the Greek-Persian wars. This marks the start of Athenian prosperity. But this was lost soon, and dispersed, since Athens lost wars trying to obtain a land superiority they did not have in mainland Greece.
It should be noted that Athens-(from around 600 BC/BCE until the middle of the 300's BC/BCE), established the world's earliest known Democracy. As far as we know, there were no other democracies that predate Athenian Democracy. One could perhaps expand the definition of "Democracy", to perhaps include, Rome's Republic, which was established around 500 BC/CE and lasted until the beginning of the Pax Romana in 27/ 26 BC/BCE-(though it would still be a stretch of the historical imagination). Perhaps even crediting the North African city of Carthage and the creation of its own quasi-democratic system shortly after the Athenians had established their own version of Democracy. Yet, despite these two notable historical examples, Ancient Athens continues to remain the birthplace of Democracy.
What is interesting is that when both scholars and students alike refer to "the Greeks as Founders of Democracy", there tends to be-(perhaps unwittingly), an ignoring of the greater historical reality. Essentially, Greek Democracy was very much a uniquely Athenian invention; there were no other genuinely democratic Greek City-States before, during or shortly after the heyday of Athenian Democracy. Nearly every Ancient Greek City-State-(whether in Greece proper, Asia Minor/Anatolia, Southern Italy, the Southern Balkans, as well as other Greek colonial city-states across the Mediterranean and Black Sea regions), were governed either by Monarchs, Oligarchs or Tyrants, whereby the citizens of those City-States had no electoral power. City-States, such as Sparta, Corinth and especially, the city-state of Syracuse in Northern Sicily-(despite the above referencing), were usually governed by undemocratic rulers and regimes. The Athenian Democratic model was quite distinct and unique within the Greater Greek world, as well as far beyond its borders.
(And while Alexander The Great may have a legendary reputation among contemporary Greeks-(as well as among fans of Greek history and culture), both he and especially his Father, King Philip of Macedon, closely resembled the Monarchical rule of various Greek City-States across the above mentioned regions and had absolutely no similarity to Athenian democratic rule whatsoever. Remember, the Macedonian Monarchy conquered Athens-(just ask the famous Athenian Statesman, Demosthenes).
So it is really more accurate to say that it was the Greco-Athenians-(from the time of Solon, until the conquest of Athens by the Macedonians), who established the world's first Democratic system-(which was far from perfect and ideal. Athenian democracy had its fair share of tyrannical and oligarchic interruptions over the centuries....as well as slavery).
Overall, the historical credit of establishing the world's first democracy should really be assigned to the Greco-Athenians....and not necessarily to the wider Greek world.