I'm primarily interested in the storyline differences between special sets and their theatrical counterparts, so here are the differences between the two (NOTE: SPOILERS FOLLOW).
The extended collector's edition runs 16 minutes 28 seconds longer than the theatrical cut, and listed below are the major differences.
1) The opening scene is different, and starts with Jake in a wheelchair on Earth, in a Blade Runner-esque Earth city. The scene moves to scenes of Jake in his apartment, then taking liquid shots in a bar. Jake's narration of "I told myself I can pass any test a man can pass" and "They can fix the spinal if you got the money. But not on vet benefits, not in this economy" are inserted during this new opening scene.
Jake beats up a bar patron who is mistreating a woman, and then Jake and wheelchair are unceremoniously thrown outside by bouncers into an alley. While in the alley, Jake meets the two RDA representatives who bring him news of his brother's untimely death. Then the movie cuts back to the original theatrical cut where Jake sees his brother's body cremated, then awakes in space.
2) During Jake's initial flyover of Pandora in his avatar, they witness a herd of Sturmbeasts, buffalo-like creatures.
3) After seeing the Sturmbeasts, Grace, Jake, and Norm stop by Grace's old English school for the Na'vi. The school is now closed, abandoned, and some walls are riddled with bullet-holes. Norm finds a Dr. Seuss book, "The Lorax", on the ground. This scene explains how Neytiri knew English so well, and certainly gives some further backstory into Grace Augustine's character.
Interestingly, The Lorax can be seen as a metaphor for the Pandoran story. Recall that the seemingly simple Seussian book is actually a lesson on the plight of the environment and industrialization.
4) We see some other different Pandoran flora and fauna, particularly with scenes of the luminescent forest floor.
5) Jake's first dinner with Neytiri is longer and extended, and it's here that she tells him her full name.
6) When Jake, Grace, and Norm first visit the Hallelujah Mountains on the way to the remote uplink station, Grace explains (in a Jake voiceover) that the mountains are levitated [via the Meissner Effect], because Unobtanium is a superconductor. There's a pretty spectacular CGI shot as the characters look around in awe at the suspended mountains.
7) Pictures of Grace and Na'vi children at her previously functioning school. Dr. Augustine tells Jake that she previously taught Neytiri and her sister, Sylwanin. However, one day, Sylwanin and some hunters destroyed an RDA bulldozer, and RDA SecOps troopers killed them at the school, which explains why the school walls were previously seen pockmarked with bullet holes.
8) Sturmbeast hunting scene after Jake tames a Banshee. After Jake successfully kills a Sturmbeast with an arrow, he and Neytiri chortle a "Heck yeah!" and whoop.
9) Jake and Neytiri's love scene comprises them linking braids together. Some kissing, nothing explicit.
10) Tsu'tey leads a war party that destroys the RDA's autonomous bulldozers, as well as the RDA SecOps squad that was guarding them. Corporal Wainfleet leads the search party that uncovers the evidence, via real-time helmet cam footage. Not sure why they cut this scene from the theatrical cut, as it persuades Selfridge to attack the Home Tree.
11) Attack of Hammerhead Titanotheres on RDA forces has been extended slightly; additional scenes of AMP-Suits getting destroyed.
12) Fight between Colonel Quaritch in AMP Suit and Neytiri on Thanator slightly longer.
13) Tsu'tey's death scene; in the theatrical cut, he falls off the RDA shuttle's aft ramp to his death. In the Collector's Edition, he falls to the forest floor, mortally wounded. He passes on leadership to Jake, and asks Jake to ceremonially kill him e.g. hara-kiri, so that Jake will be the last shadow that Tsu-Tey sees. Jake does so.
I preferred the original Tsu'tey death scene, which was more dramatic. Jake, had afterall, already become the de facto clan leader by that point in the movie, so further formal transfer by Tsu'tey (a minor character) seemed unnecessary.