It is not only historians who decide. Usually, the "Allies" call such themselves.
For example, you refer to World War I. Please remember, that on the very beginning there were two blocs: Triple Entente (France allied with Russia along with United Kingdom, which was not allied to anybody, except the Commonwealth), and Triple Alliance (Germany allied with Austria-Hungary, along with Italy, which was allowed not to fight against the UK).
Because later the Triple Alliance had been increased by two countries without Italy, making Germany, Austria-Hungary, Ottoman Empire and Bulgaria, they referred to themselves as Quadruple Alliance (refer eg. Treaty of Brest Litovsk, articles 2, 5, 6 and so on).
The other countries were called the Entente (without "triple", as more countries joined, mainly Serbia, Belgium, Italy, Romania and the USA, but also eg. Portugal and Japan), but as far as I remember, there were no official term "the Allies" for this (they are called "Allied and Associated Powers" in The Versailles Treaty, but this is to distinguish them from Germany, the other party of the treaty).
Calling some countries "the Allies" is used when they are different from one another (they have different locations, different language etc.). This applies more to France+Russia+UK than to Germany+Austria. So using "the Allies" for them is more language-friendly than for these German countries (even if A-H was a multi-cultural country, it was more German than any other, even Hungarian). Germany and Austria were considered similar and it was somewhat natural in 1938 during the Anschluss.
During Napoleonic wars it was analogous, as France had only vassal allies (Duchy of Warsaw and the others were conquered or forced in other ways to join), while Great Britain, Prussia and Russia (main opponents) fulfill the "requirements" to be "the Allies" as they are different from one another.
The same applies to WW2, with UK, France and Poland having at the beginning mainly one opponent (Germany) along with her minor vassal (Slovakia).
I would say that using the term "the Allies" depends on how different the forming countries are. If they are more similar than the other side is, they are not the Allies.
It can be also affected by British Commonwealth which can be considered as a worldwide alliance with countries like Australia, Canada, India, South Africa and several more or less independent lands. So it is easier to call a bloc with the UK as "Allies".
Also, the United Kingdom, liked the term "the Allies", to express her independence from other countries. They are allies, equal parties of a treaty, but it is a form of good business. The treaty ends and they are not allies anymore, and any other country can be, even a former opponent. This attitude dates (with some exceptions) since the end of the Hundred Years War, and was given a name "Splendid Isolation" in 19th century. That is why it is somewhat natural now to refer the "UK-side" as "the Allies".
However, in my opinion, all of this should apply to WW1 only in common language, as "the Allies" were in fact the Central Powers.