To be fair, every iteration of GITS has been different.

In the manga, Kusanagi was very anti-authoritarian, very much the spunky, sexy, "fuck you, old man!" sort of character. (Believe me, the difference is jarring. It really makes you wonder how the character progressed to the one you see in the anime.)

In the movie, Kusanagi was more reserved, even sullen. You might even say depressed. The story revolves around her being in the midst of an existential crisis, which drives her to shirk the chain of command in order to commune with the Puppet Master.

In SAC/2ndGiG Kusanagi has always struck me as a consummate professional. She is the best at what she does, practically a force of nature. She is a highly capable leader, and not at all prone to flying off the handle chasing after existential answers or being comically defiant.

The other characters get this treatment as well. Aramaki in particular... SAC/2nd Gig Aramaki is the man- he has the connections and the smarts. He knows the big picture more than anyone. Movie Aramaki is... deflated. It's clear that he has been at this for a long time and it is wearing down on him. "Another puppet from our friend the Puppet Master..." he sighs. In the manga he is more of a foil for Kusanagi than anything. Borderline antagonist. I don't remember the details but IIRC Kusanagi doesn't end up working for Aramaki willingly...

Try to think of GITS as being a little bit like Doctor Who, if you like that show. The names stay the same but each new iteration of it is something different.

I can't really speak to the quality of Arise yet, it's still on my to-watch list... But I have always found the differences between them to be pretty interesting.