There are two wrong assumptions in the question: (a) Athens isn't still a major Greek city and (b) Sparta was never a major Greek city.

On point (a), it may be tempting to look at Ancient Greece and modern Greece, see Athens being a prominent city in both, and conclude that there is continuity. But this is misleading; there is a huge gap between these two data points. For most of those two thousand years, Athens was not a major city, or even a city at all.

Already by the 3rd century AD (after the devastating sack of the city by the Heruli) there was little left of Athens' former splendour. During the Byzantine and Ottoman periods, Athens shrunk to a village of a few thousand people, mostly herdsmen, living in the shadow of the ancient ruins. There are some wonderful drawings of these ruins by 18th and 19th-century travellers, who had an unspoilt view of them because the countryside around the Akropolis was basically empty.

Athens only resurged as a city after the establishment of an independent Greece in the 19th century. In 1834 the new nation-state chose Athens as the site of its capital, in line with a general nationalist programme of disowning more recent history and claiming direct descent from the Classical Greeks. But even then, the explosion of Athens to its current size (with about a third of all citizens of Greece living in a single city) dates to the 20th century, starting with the influx of ethnically Greek refugees from the new state of Turkey.

As to point (b), the ancient Greeks themselves already remarked on the contrast between Sparta's power as a state and the unimpressive size and appearance of its urban centre. Thucydides famously remarked that if future humans were to find Sparta's ruins they would never believe it had once been the dominant state in Greece. Throughout the period of Sparta's greatest power, the "city" consisted of an agglomeration of 4 villages (with a 5th a few kilometers distant), made up of simple mudbrick houses. There was almost no monumental architecture until the Hellenistic period, when Spartan power had waned and the city came to resemble typical Greek settlements elsewhere. There was no measure on which the town of Sparta (as opposed to the polis of Lakedaimon) could ever count among the great cities of the Greek world.

In any case, the Greek town of Sparti* is a modern resettlement. Ancient Sparta was abandoned in the Medieval period and the town's modest ruins lie just north of the present-day city.

 

*) Despite the different vowel, the name of the city is the same (Σπάρτη). In the Classical period, one of the distinctions between Dorian Greek (spoken at Sparta) and Attic Greek (spoken at Athens) was that many instances of the long vowel η (ē) in Attic Greek were pronounced with α (a) in Dorian. Our surviving sources, which were mostly written in Attic or Koinē Greek, tend to speak of Σπάρτη (Spartē), but modern historians invariably adopt the Dorian Σπάρτα (Sparta). In this case, modern Greek adopts the Koinē Greek spelling, but the pronunciation of the vowels has shifted, and nowadays the long vowel η is pronounced i. Hence Sparta, Sparte and Sparti are all the same name, as pronounced in different dialects and forms of Greek.

This was VERY interesting, thank you.