There are two main categories of being special to me.
The first is when characters show some maturity - or just a lack of stupidity - in their thoughts and behaviour in the first episode. Some examples include:
- Thors from Vinland Saga
- multiple characters from Frieren
- now that I think about it, plenty of anime from my Peak Drama list fits this criterion
These anime would end up having stories, characters and writing that are top-notch, clearly a cut above the rest.
The other is when the show subverts expectation by not following stupid tropes from the start; these are usually parodies. Some examples include:
- Cautious Hero - dude who got isekai-ed isn't some loser to begin with (i.e. no wish-fulfillment)
- Konosuba - dude who got isekai-ed did not get cheats (i.e. no power fantasy)
- 100 Girlfriends - dude with a harem is not a wimp who can't handle girls (i.e. no self-insert for losers)
These anime are special by virtue of being different from peers of the same genres / subgenres.