Except the Ember Island Players performance is unintentionally hilarious with how they got the details wrong, and they sort of slipped in some sly jokes for the fans that had been watching the show (for example: "Oh, look! The Great Divide!" "Let's just skip it.") It's a bad adaptation of things that happened, but it can be considered fun to watch.
Shyamalan's movie was not fun in any way. I am a big fan of Avatar: TLA, but even if I wasn't, I'd still probably think this movie was badly acted, badly shot, and DUUUUUUUUUUUUUUUUULL. Why should I care about "Ahng"? He seems depressed all the time, and he just kind of goes with the plot because... it's the plot. None of the characters in the Shyamalan movie are really developed except maybe Zuko and (kind of) "Ee-roh".
Little details that follow the show being wrong might piss off fans (they kind of bothered me but not to the extent that others were bothered by it). But the movie completely and utterly fails to capture even a sliver of what made the show exciting. Hell, I wouldn't even have minded if the characters changed as long as they changed into... something. Aang may not have been a girl or Peter Pan, but that was at least something neat to watch. Shyamalan must have invented some kind of sponge that somehow drains whatever it touches of anything resembling liveliness, and he tested it out on the written outline of Season 1 of The Last Airbender.
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And now, for a fan's complaint, HOW THE HELL DID THE FIRE NATION CONQUER THE WORLD IN THE MOVIE VERSION?! Unlike the cartoon, where Firebending is treated more like bending the energy around you (which is why they can conjure fire anytime), the movie nerfs Firebenders so that they can only bend from burning flames (supposedly). That sounds even more horribly situational than Earthbenders needing earth around them in order to bend (a limitation Toph and later generations learned to overcome). You'd think that the other nations could easily stop that by extinguishing their flames if the Fire Nation attacks: drown out the campfire, bury it in dirt, or blast it with an intense gust. It seems that in the movie version, Firebending should be the weakest, most situational form. How could they possibly commit genocide in that condition? My only theories are that either the Fire Nation armed forces are full of smart people, or everybody else in the other nations is incapable of basic self-preservation tactics.
At least in the cartoon, Firebending translates to "turning the heat and light around you (often provided by the sun) into fire or lightning". So it makes sense that you could shoot fire or lightning at just about any time because that energy is around you (or within you) quite often.
That's like my second- or third-biggest complaint about the movie, tied with "that scene with the Earthbenders" and losing out to "It's so boring."