1.
Great: (1) big; large (2) More than usual; much (3) important; remarkable; famous (4) most important; main; chief
Favorite: adj. liked better than others; liked very much. n. (1) a person or thing liked better than others; one liked very much (2) a person treated with special favor.
(These don't have to be seen as strict, rigorous definitions, and can be thought of as being guiding ideas that are reasonably close to common usage.)
2.
"Great character" often, but not always, elicits the thought of a strong character with noble or "positive" goals. If we continue to name more great characters, we'll then move on to characters with more pronounced "negative" traits: selfish, ignorant, brash, etc. In other words, we tend to see those glowingly positive traits first, then the negative ones. Hence, we'll probably see someone mention someone like Goku, Sailor Moon, or Astro Boy before mentioning Gendo Ikari, Light Yagami, or Balalaika. Mention great leaders, and we'll probably see Martin Luther King, Mohandas Gandhi, and Mother Teresa mentioned before Mikhail Gorbachev, Margaret Thatcher, and Napoleon.
3.
"Your favorite" is a slightly more personal term than "The greatest" - your personal fondness, your attachment. When you offer up the greatest, you're offering a single person, character or thing to be judged publicly by others according to certain standards (the standards varying, of course, and always open to further refinements). When we favorite, we're not exactly offering our valued, our special other, to be judged. Our valued can remain our private, intimate affairs. Greatness more often than not focuses on a remarkable trait, something that allows the character to outshine, outperform others in a way that begs to be publicly celebrated. (If Beethoven's 9th was played only once in an empty theater and never played again, would it be great? Perhaps even better: would we have any reasons to call it great?)
4.
Hypothetical poll question: "Who is the favorite character of all time?"
5.
"Because Yuki Nagato types faster than almost anyone else, we judge her to be your favorite" is a strange thing to hear. It's just as strange as hearing "I think x is great because x died."
6.
Perhaps, the concept or word "greatest" is a public word, while "favorite" is much less dependent on outward criteria. "Favorite" resides happily as a private word, as it were.
7.
If we keep our valued inward, then we can in some sense see favorite and greatest as being realizations of a single concept or "nature". And it's in this private space where the distinction between the two is easily thought of as being entirely subjective. There's no one else to agree or disagree with if I say Goku from DBZ is the greatest character ever. If I say this in a public forum or discussion, then someone can corroborate this by producing One Piece as counting towards my claim since Eiichiro Oda was heavily influenced by Akira Toriyama's creation. Someone else might show me his Goku tattoo. Another might produce DBZ party accessories like paper towels, cups, and plates, all this showing how much DBZ has a place in Western culture. Others can dismiss this by saying that it's popularity working here, not greatness (which is another related argument). But when someone favorites Yuki Nagato, his happening to have many Nagato related memorabilia isn't meant to be offered to the public as "proof" of how much he admires her (even though it can, in some informal sense of "proof"). His admiring Nagato doesn't need to gather second-party objects and doesn't need to require third-party judgments and evaluations.
8.
Greatness is always at sometime or another accessible, public, open to general scrutiny. In some of the most remarkable cases, greatness involves creative acts which demand the public's attention; they animate all those who experience such acts. Greatness can bring solidarity. A favorite doesn't really demand or require availability. Usually, we're more than happy to offer our favorites and see the favorites of others, but we're not offering them to be judged, evaluated, or compared in the hope that such offerings will compel us to adopt new favorites. (Our MAL lists show rank, but we do that ranking after we've seen the shows. We don't actively watch Kanon and Air at the same time, and balance the pros and cons to decide which is our favorite. We don't even need such lists.)
9.
Greatness can stand alone in the sense that the thing need not always be popular, always in the public eye; it doesn't have to be everyone's favorite. If anyone sized up Leiji Matsumoto's work, they'd likely call him great even though they never heard of him 'til then.
10.
A favorite can stand alone, too, in its own way, which can be noticed by the shift in language: we often judge greatness because it is greater than something else (it's right there in the word itself); however, I value my favorite as being intriguing, compelling, singular, perhaps even ineffable. The "liked more than..." isn't the same sort of relation as "greater than...". Often, we don't even bother with those sorts of relations at all (see 5.).
11.
Some candidates for greatness force redefinitions of the concept itself - great people can be complete bastards. If he had been otherwise, would he still have did the things he had done? Created the monumental achievements he did, e.g. Beethoven and his 9th? (Here was a man who often forgot to put on his happy pants in the morning.)
12.
Notice that both favorite and greatest don't require their instances to be essentially or entirely positive. We can readily accept the negative into our definitions of favorite and greatest. Some characters may in fact undermine, cast off, or violate some values we would normally call positive. It might even be because of their human failings or moral shortcomings that they are so captivating - they compel us to dwell on our own values.
