No word can be substituted for "equal" in that Animal Farm commandment without completely changing its meaning
You know the one? "All animals are equal, but some animals are more equal than others."
My partner recently made the following half-joke: all people are cool, but some people are cooler than others. The thing is, some people can be cooler than other people (case in point, me and him! I'll let you figure out who's who) so his joke ended up sounding like a completely ordinary observation, totally undermining his point and destroying any resemblance to the original. Let's try to construct a synonymous phrase without using the word "equal".
Perhaps what we need here are adjectives that cannot be compared. "Cool" does not work because we could theoretically rank each person on the planet by coolness. So let's try another one: all people are alive, but some people are more alive than others. Is a person still a person once they have passed away? Let's set aside this ontological debate for now and suppose that we're only talking about living people. The quote ends up sounding just like a classic inspirational tweet, describing a timeless sentiment in a unique arrangement of words that makes it seem novel. Seize the day! Do things you love! Live life! Set yourself apart from the herd. It's a nice thought but it bears even less resemblance to the original.
Let's try a close synonym to "equal": identical. All animals are identical, but some animals are more identical than others. When we say two beings are identical, we might be referring to twins, or best friends, or maybe a parallel self, and in all these cases we mean "equal in many respects". So the sentence loses all meaning here unless you really force it (groupthink? or clones??).
Reading this latest version, it becomes clear that when we're saying two beings are "equal" like we do in the first part of the quote, we typically mean "equally worthy", not "equal in all respects". On the other hand, the second part of the quote implies that equality is worthiness, and that some animals are more worthy. For the phrase to have the same sardonic ring, we first have to describe a standard that must be applied... well... equally, and then twist its meaning to imply that some beings are more deserving of that standard than others. We make it sound like this standard could be applied in different quantities, when doing so would actually undermine the standard itself (not to overexplain the joke, but being more equal than somebody else implies that you are in fact not equal). So let's pick some rights that should be applied equally to all sentient beings.
Okay, how about this: All animals should be free from discrimination, but some animals should be less discriminated against than others. We had to change the phrasing entirely, but that's the right idea! Or how about: All animals have the right to privacy, but some animals should have more privacy than others. Bingo!
Still, "equal" is special because it implies worthiness, and I can't think of a word that has the same double meaning. So we can conclude that "equal" is a load-bearing word in this classic quote. We cannot remove it without losing the essence of the sentence's meaning, but that doesn't mean my partner's joke didn't land. It was, like all jokes, deserving of the heartiest laugh.