On the higher quality end of the spectrum, I think one of the main differentiators is just how seriously the staff takes the production. They lean into the cinematography, storyboarding, directing, music, choreography, etc just as much or more as one might expect from western live action prestige TV. This is exceedingly rare in TV animation in the US and is only really seen in our animated movies (which are rare these days, at least in 2D form).
The other thing is that high quality anime is exceedingly good at building atmosphere and creating vibes. Half of the enjoyment of Cowboy Bebop for example is just basking in the ambience.
To be fair, most Japanese anime is also meant for kids and teens, but they were willing to explore content that would absolutely shock Western parents (violence, sex, nudity, as well as more nuanced stuff like sociopolitical commentary).
Is this different today? I feel modern Japanese anime is more toned down compared to say, the 1990s, while non-Japanese animation has been “toned up” in content.
The anime community has, for as long as I've been a part of it (13 years or so), decided that anime is "animation made in Japan". This heuristic has actually worked pretty well.
But the lines are increasingly blurred.
- Japanese produced shows are outsourcing some animation to China and Korea, and sometimes taking direct funding and story writing input from the USA.
- Non-Japan produced shows are taking notes on what works, drawing on it for inspiration, and in rare recent cases even outsourcing animation directly to Japan.
- There is a TON of money in gacha games, and the biggest "anime" titles some people may recognize are gacha games, butand the majority of those are run 100% by Chinese companies. Ironically, sometimes sending them over to Japan for the TV adaptation.
Just like food: Italy may have "invented" pizza, but New York pizza is now its own thing.