I will admit the movie is badly shot, written and directed, but it wasn't a page for page adaption, it dared to stray from the original series' very overdone plot, which, hell I love it for. It did drastically different things from the series from which I liked. because if I wanted to see page to page adaption, why not just watch the series?
Let name name off why I like it:
Why would Aang instantly see Katara as Den mother? A Den Mother is: the female of the team who will comfort the team and support them like a real mother. In the show, he instantly does this after his first Avatar state freak-out, but in the movie she is his friend but no where near the Den mother. she is visibly afraid of his avatar state the first time it appears. because "HEY THESE THINGS NEED TO BE DEVELOPED OVER TIME", no one ever questioned this during the TV show because it just seemed to fit, but in the movie it would make no sense.
The show never directly addresses the fact AANG KILLED PEOPLE, in the finale of Season One, he goes on a rage and slaughters 50+ fire nation soldiers. It is never brought up, the only thing that is brought up is that Aang lost himself, but never "hey their deaths aren't your fault". The movie avoids that this by having the Avatar State being non violent, which leads into my next point.
It gives new dilemma, Aang in the series has his Avatar state go rage and that was a big point of Season 2. In the movie it flips this and makes Aang's normal state dangerous to the point his body bends more than he wants to(He tries to bend about a cup of water, he'll end up accidentally bending a whole homesized pool(this happens twice in the movie), making you wonder if or how he'll control this.
Those and little touches, the Avatar Test by both Iroh and the Airbenders, showing Katara mess up as she has had to learn by teaching herself, having the Avatar's presence seem like a big deal (which was RARE in the show, only 1/10 people would freak at knowing he's the avatar the other 8/10s would simply ignore him or try to use him in some way, the other 1/10 had a bone to pick with him about his past lives) to have the people do a special bow and having it seem validated by him returning a bow.
To me the animated show is a run of the mill story with beautiful animation and decent voice acting, that bastardize and changed a lot of Eastern philosophy(There's no mention of origins but yet it's known that alot of Chinese spirital practices are from the west half of asia like India especially), the movie while badly written and directed did something different it made and gave an interesting twist, not ignoring the real roots of these philosophies and didn't just make everyone a character in the bad way.