What I'm interested in looking at is a specific criticism of Avatar. What people often say is that it's either Pocahontas or Dances With Wolves in outer space. There are some similarities in plot, but when you get down to it, it's actually closer to an entirely different movie.
The Mission was a dramatic period piece released in 1986 with Jeremy Irons and Robert De Niro. Irons plays Father Gabriel, a Spanish Jesuit missionary tasked with converting a South American tribe. He journeys into their land, climbing a waterfall in the process, and manages to gradually win them over with music from his oboe. Meanwhile, De Niro plays Rodrigo Mendoza, a slave trader who captures and sells the natives of the region. That changes when, in a fit of jealousy, he kills his brother. Riddled with guilt, Mendoza seeks redemption by becoming a Jesuit and joins Father Gabriel and his fellow priests at their new mission. Things seem to go well at first, until certain political developments in the relationship between Spain and Portugal threaten everything.
Now plot-wise, Avatar may be closer to The Mission than either Dances With Wolves or Pocahontas. Let's break down the basic plot. In both cases, the basic set-up is similar. You have a character who is basically sent in by an authority to live among a native population for the ultimate benefit of their superiors. In Avatar, Jake Sully is working for a corporation, while in The Mission, Father Gabriel is working for the Church.
So in both cases, our heroes venture into the territory of the native population and gradually win their respect. In fact in Avatar, there is even talk about Grace running a school for the natives, essentially a mission of sorts, though the fact that Jake Sully does become integrated into their society is a bit reminiscent of Dances With Wolves.
This brings us to the next big development in the plot of each. While our heroes are spending time among the natives, their superiors are making decisions that don't take them into account. In Avatar the conflict is driven largely by a desire to recover a valuable resource which is in high abundance under the tree where the native tribe is living. In The Mission, the Spanish government is offering the area to that of Portugal, with Cardinal Altamirano (Ray McAnally) being sent in to make the difficult decision of whether any missions should be left alone.
Either way, the authorities come to desire the land, and want the native tribe out of the way. The one thing that stands in the way is the protagonists, who have come to sympathize with the tribe and eventually decide to take action.
This brings us to the climax of both films. Now granted, in Avatar, the final battle and the initial invasion of the natives' home are spaced out, but they're still similar in structure. In either case, the authorities resort to violence to get what they want, and the protagonists attempt to make a stand. The result is a massive bloodbath with extensive casualties on both sides.
Now technically, the outcome is slightly different in each film, but in either case, most of the cast is killed one by one. In Avatar they do ultimately triumph, though with most of them dying in the process, while in The Mission the protagonists put up a tough fight but are ultimately massacred by the invading Portuguese army. Still, both films see the heroes standing up for the native tribe against seemingly impossible odds.
I won't make any judgments about Avatar regarding whether this affects it as a film, but if you look closely, the resemblance to Dances With Wolves or Pocahontas isn't as overt as some make it out to be. The truth is that while there are similarities, the story of Avatar is far closer to The Mission.