Despite its simple theme of Jake's spiritual awakening, I think the CGI does a lot to accentuate this particular aspect compared to other stories mentioned -- Pocohontas, Dance with Wolves (which I didn't really care for). If anything it brings more focus using more visual cues that Jake is undergoing incremental changes. The external transformation mirrors his internal transformation which is brought front and center to the audience's attention by the CGI.
For example at the beginning of the story, Jake was a crippled and broken human, suffering physical loss as well as the emotional loss of his twin brother whose spot on the Pandora mission he inherited. Even after arriving on base, he didn't measure up to standards to either of his superiors. However when he was found to be of value, he was now used for specific objectives.
Even when Jake was given a Na'avi body which mitigted his physical disabilities, he, emotionally, was still no different from his original human state. He still behaved and dressed like a human. However as he was taken in by the Na'avi tribe, the CGI colors accentuated how Jake began viewing the world. He found it a much lovelier and livelier world than he had ever noticed compared to the beginning of his journey. Facial expressions can be seen on the animals as he bonded with them, and his dexterity improved dramatically. During this portion of the movie while his physical abilities grew, he emotionally understood what it was to be a citizen of Pandora. While he was human, his view of the world was myopic, but as a Na'avi, he saw and appreciated and eventually embraced the spiritual interconnectivity. By the end of the movie, it is very clear that Jake, internally, was wholly a different person, even before the change was made permanent. And of course, he was much happier. I think the CGI really made the audience, not just see, but feel this transformation as it was happening to Jake. And it made for a very satisfying story.