The central notion behind your question, of being "less/more varied", could maybe refer to something meaningful and testable, but the claim that Hungarian is "more nuanced" than English, or that creoles are "clearly less varied and lack the expressive power of ancient languages" (like, Latin, Greek, Arabic, Sumerian, I would suppose), or that Spanish and Italian are "less varied" is lacking in empirical support.
The linguistic domain that you're roughly pointing to is crosslinguistic semantics. If you want raw variation, English has the terms "sofa, couch, davenport, divan" which refer to the same object. I imagine there is some similar situation in Hungarian where there are 3 or 4 words for the same thing where English has 1. English also has the words "knife, machete, sword", but they refer to similar things, not the same thing. So you need to clarify whether you are looking for sets of semantically-related words, or absolutely identical words. And you need to also clarify whether you include social-register distinctions, since there are many verbs referring to the sex act and nouns referring to male anatomy in English which have different social consequences -- connotation rather than denotation. So what distinctions are you asking about?
Based on your later replies, I think I understand the distinction you're looking for. Words and morphemes can be organized hierarchically in terms of what things / actions / states they refer to. For instance, "mammal" refers to a very large set of warm-blooded animals, and the term subsumes "goat", "reindeer", "sheep" and other things under one word. In English, we just have "reindeer", but in North Saami, there are dozens of terms for reindeer depending on sex, age, and body properties (there is also a general word boadzu that simply means 'reindeer'). Thus the entities identified by "reindeer" in English can be further subdivided by selecting one word vs. another in N. Saami, and N. Saami has a "more-nuanced" vocabulary for reindeer: the set of real-world things identified by English "reindeer" can be further distinguished in N. Saami by selecting other words. Similarly, in Somali, there is a word ari which refers to goats and sheep, so English is "more nuanced" in terms of these animal identifications (there is no common English term generalizing over goats and sheep, though there is a Latin terms that biologists can use, Caprinae). The Somali term *ari *is a superset of goat and sheep.
This kind of subset / superset analysis can be applied to any collection of words and morphemes, hence 3rd person pronouns may simply be undiftinguished "3rd person", or they can be further distinguished "singular and plural", or "masculine and feminine", and that allows further distinctions "masculine singular", "feminine plural" and so on. There are many, many ways of subdividing concepts. English pronouns distinguishes between male and female singular 3rd person referents, and Saami does not.
Languages do not differ in their net expressive capacity, so where they can use a single word-choice between vuonjal and varit, we would have to use phrases like "female reindeer between a year and a half old and two years old" and "male reindeer between a year and a half old and two years old".
I don't see any realistic hope of computing a general "degree of nuance" value for two entire languages (nor do I see that it would tell us anything about the languages -- just because you can define a function doesn't mean that it refers to something useful). One problem would be in comparing a tense-based inflectional system versus as aspect-based system. In the cases of 3rd person pronouns, reindeer, and goats, we were dealing with subset relations in the referents, but the things that perfective / imperfective refers to is incommensurable with what past / present / future refers to.