There are two types of advantages.
A comparative advantage is when you have or can produce more of something than someone else. (Person, country, whatever.)
An absolute advantage is when you have or can do or produce something others can’t. This can be threshold matter: in World War II the Allies had more than enough oil and the Axis didn’t have enough to run their war machine. While in numbers terms it looked like a comparative advantage, it was actually an absolute advantage: it strangled Axis production and their ability to field mechanized troops, aircraft and ships. Up until the nuclear bomb, in terms of tech, the opposing great powers were about equal, but in terms of the key resource required to run everything, the Allies were in surplus and the Axis never had enough.
Firearms were an absolute advantage. Once they spread, European firearms were usually still better and Europeans understood how to use them properly, while their opponents rarely did. Cultural understanding is often necessary to get the most out of a technology. In India, the British East India company often faced off against Indian armies with the same weapons as them, but they deployed them atrociously: they didn’t know how to use them properly.
Machine guns, when first deployed, were an absolute advantage. The Maxim gun, deployed in Africa, let British troops defeat armies literally 100 times larger than it.
Horse archers, properly deployed, were an absolute advantage. Genghis Khan didn’t just united Mongolia (making many tribes all into Mongols), he changed society and military organization and how horse archers were deployed. For about a century the Mongols were essentially undefeated, creating the largest land empire in history, and when the first real loss happened, the Mamluks inflicted it by using a Mongol style army effectively against the Mongols.
The steam engine plus factories produced goods in such quantities that it was a relative advantage which become an absolute advantage. Factories had existed before steam, indeed we have evidence of factories in India before the Aryan invasion, thousands of years ago. But add steam, and BOOM. (Oil and electricity merely increased production, but they weren’t the quantum leap.)
In the invasion and conquest of the Americas, the absolute advantage wasn’t cannons and firearms nearly so much as it was European diseases, which the Europeans had some immunity to and the natives had no immunity to. End result, 90% of the population killed off by disease. Without that Europeans might have done an “India” and conquered various North American areas, but they would never have been able to colonize all of it and drive most of the population to extinction so they could keep it in the long run.
Cannons were an absolute advantage for a time. The monarchs of the early Renaissance were able to use them to reduce the noble power massively and turn them from semi-independent rulers (feudalism) into aristocrats dependent on the king, since castles could no longer hold out in sieges for any length of time.
Further back, the European Knight had an absolute advantage over peasants and most European infantry (minus the Scots and Swiss and a few exceptions.) That advantage didn’t extend much out of Europe. Knights were better than Byzantine cataphractoi and Muslim cavalry, but not so much as to allow lasting conquest. However, against internal enemies in Europe, their superiority was massive, especially against peasant armies.
Absolute advantage is about having something or being able to do something your competitors don’t have or can’t do. The current imbroglios over computer chips and airplane manufacture are the West’s attempt to keep the few places where they still have an absolute advantage over China, since they’ve given (sold) the rest to China, and lost most of their relative advantages.
In eras of absolute advantage, small societies can do astounding things. The Mongols conquered vastly more populous areas and so did Europeans in general and the British in particular.
Eras of relative advantage, on the other hand, are eras of the most and the biggest.