So after I watched the live action twice and I started the anime, I do have some initial impressions about the differences. Not the plot differences, but more thematic and characters defining.

First, the writing of the live action is far more superior than the anime, at least at this stage of the beginning while I am still in the first season. The anime is more childish and spends long, long time on really unnecessary stuff. There are a lot of monologs when some character is just talking and expressing their thoughts. The action is disconnected and fragmented, jumping from one thing to another, a lot of moments are just exaggerated. So the anime reminds more a children cartoon and it's really far from the more serious and darker live action. But since the world building is great and very promising, it's still enjoyable, although some moments are just a waste of time. Hopefully it will improve in later seasons.

Second point is that the characters are also less childish in the show. In the show they are more adult in age, more mature in thoughts and motivations, more serious and more grounded. Maybe it's too early to judge and I know that the characters grow up in the anime by years from the start. Still, the point in life when we meet each in both the show and in the anime are quite different. And I do like it more what the show did with them. In the anime they still feel flat and one dimensional, there is still no significant baggage behind them.

And third, the character of Luffy is crucially different in one part. In both anime and show he is goofy, fun and optimistic child, with clear morals and clear distinction between good and evil. There is also some minor darker side to him as well, he is not fooling himself about the world and how bad the pirates can be. But the show adds him more depth and it makes him even more interesting as a person. And it is not some smaller details, like taking the job of the captain and the leader of his crew more seriously. And it is not his naivety about grownup stuff, like sexual references. I think the most crucial addition to his character is that in the show he is a great salesman and very good at convincing people in something that they need and to manipulate them to do something for his own cause. The show is not even hiding it, but it is completely missing in the anime. He can recognize and appreciate wisdom, manipulations and sophistication because he is also like that. This is different from the more simple minded Luffy of the anime. I think it adds something very mature to his character and makes him more ominous in general and intimidating when he needs to be. This is great stuff from the show writers, they were able to recognize the need to add this to his personality and it works.