Paul W. answered 12/17/20
Dedicated to Achieving Student Success in History, Government, Culture
Keeping in mind that the conduct of warfare, which is the means by which one builds an empire, is governed by uncertainty - in other words, there are virtually no guarantees when it comes to waging war - one can only talk in terms of the likelihood of possibilities.
With this in mind, for a number of reasons, the Kingdom of Macedonia would be - indeed, was - better suited to conquering an empire than the city-state of Sparta. Sparta was a society governed by exclusivity and its 'foreign policy' was, to one degree or another, isolationist. The two went hand-in-hand. Spartan society was built around - and governed by - a very exclusive warrior elite that devoted their lives to preparing for war and little else. This warrior elite comprised a minority of the population, ruling over both free non-warriors, who fulfilled a variety of necessary functions (for instance, craftsmen) - and a large number of 'Helots' (slaves). The warrior elite controlled all political power and feared the influence of ideas from other Greek city-states, where, to one degree or another, political power and the rights of citizenship were NOT limited to a warrior elite. In short, the Spartan warrior elite did not want either the free non-warriors or the Helots, who made up the majority of the population, to be inspired by the ideals of the other Greek city-states to challenge the warrior elites' monopoly of power. The Spartan warrior elite believed that the best way to prevent this from happening was to have as little to do with the other Greek city-states as possible, thus the policy of isolationism.
Clearly, conquering an empire is the opposite of isolationism. Therefore, it's no accident that, after Sparta and her allies won the Peloponnesian War (431-404 B.C./B.C.E.), the Spartans did not make much of an effort to maintain their control over the defeated Greek city-states. Instead, Sparta returned to its former isolationist policies.
But, even if the Spartan warrior elites actually wanted to conquer and rule over an empire, this would have been difficult due to another factor, manpower. Spartan warriors did not live with their wives until late in life (living, instead, with one another in barracks) and this contributed to a low birthrate among the families of the warrior elite. In turn, those male children born to warrior elite families would undergo a training regime that was so extreme that many would fail to become warriors. As a result, the number of warriors available to serve in Spartan armies declined over the centuries and, therefore, the military power of Sparta also declined with the passage of time.
By contrast, while the Kingdom of Macedonia was, as the name indicates, ruled by a monarchy, so that political power was monopolized by a royal family, unlike Sparta, Macedonia was neither exclusive nor isolationist. Instead of isolationism, the kings of Macedonia actively pursued the adoption of ideas from the Greek city-states - the future Alexander the Great, for instance, was tutored by the Greek philosopher Aristotle. King Philip (382-336 B.C./B.C.E.) adopted the best ideas from the Greek city-states in order to modernize Macedonia and, in particular, create the best army for its time. Through a combination of natural resources and flourishing trade, King Philip could afford to maintain (pay the wages of) a full-time, professional army whose size, unlike that of Sparta's, was only limited by the kingdom's wealth.
Philip's successor, his son Alexander the Great, was even less exclusive and isolationist than his father - the very opposite of the Spartan warrior elite. As Alexander conquered the territories of the vast Persian Empire, and beyond, he adopted cultural aspects of the peoples he conquered, encouraged through personal example the intermarriage of the Macedonian and Greek officers and soldiers of his army with the conquered peoples, and employed non-Macedonian / non-Greek officials and soldiers in his empire and his army.
In short, the Macedonians had both the motives and the means for conquering an empire - demonstrated by the fact that, under Alexander the Great, they actually DID conquer an empire - while the Spartans had neither the motives nor the means to conquer an empire.