Both stories involve a civilization invading another civilization for resources. In Avatar, the corporation, with the help of the military, is searching for unobtainium- an incredibly rare mineral. In Things Fall Apart, the British are planning to mine and drill for oil in Nigeria, but their primary goal in the novel is missionary in nature. They are seeking to build a strong Christian foundation among the Ibo.
The indigenous societies fight against the invaders in both. However, in Avatar, a human steps in to lead the native army against the human military. There is no such figure in the novel; instead, Okonkwo leads his own revolt against British rule. That seems to be a mojor difference between the two. In the novel, Achebe spends a great deal of time establishing the Ibo culture, showing how everyday life works in their society. In the movie, we don't see the Navi culture- except through the eyes of the human interloper(I can't remember the character's name). Things Fall Apart is much more focused on the Ibo culture and its response to British colonialism, rather than a simple adventure/love story.