The Movie: Smaug's attack is told by Bilbo, as a sort of prologue to the Red Book of Westmarch. Bilbo starts by telling us about the wonders of Erebor, its gold and gems, and of course the Arkenstone itself. Thror, Thorin's grandfather and the King of Erebor, had become sick with greed - and this brought the attention of the mighty "firedrake from the North." Thorin himself calls the alarm, as Smaug rains firey destruction down on the town of Dale, then turns his attention to Erebor itself. As Thorin leads the dwarven defense, Thror is seen hastily grabbing his prize, the Arkenstone. Unfortunately, the dwarven army fails, Thror loses the Arkenstone, and Thorin is forced to physically drag him to safety as Smaug claims the riches of Erebor for himself. Outside the front gates, as dwarves flee for their lives, Thorin sees, at a distance, an army of elves being led by the Elf King Thranduil. Thranduil, ignoring Thorin's pleas for help, turns his army away.
Any excuse for him to practice that creepy head tilt.
The Book: Thorin tells the tale, not Bilbo, and he does so during the supper the dwarves all have at Bag End. The immense richness of Erebor is still mentioned, especially its "marvelous and magical toys," though no mention of the Arkenstone is made at this point in the story. Also absent is any indication of Thror's intense greed. Smaug still attacks Dale, but only after he defeats the dwarven army outside the front gate (instead of them meeting him inside). The battlefield is covered in fog, as Smaug's fire evaporates the rivers of Dale into a great steam. Thranduil and his army never arrive, and in fact are never even mentioned. Thorin's role is much smaller in the book. He isn't even present during the attack; it happens while he is out adventuring, and he sees it from a great distance. During Smaug's attack, Thorin "wept in hiding."
What does it matter? Thorin's differing roles is pretty huge. In the movie, he sounds the alarm, leads the attack, leads the retreat, and personally saves the life of the King. In the book, he... hides and cries. This provides the audience with a more heroic, likable character to get emotionally invested in.
Fighting dragons > sobbing in the fetal position. It's an objective fact.
The inclusion of Thranduil is a bit more complicated. The elves of Mirkwood were close to Dale and Erebor, but not close enough to march an army down in a few hours notice. While there's all sorts of help they could have offered to the dwarves, and they didn't (at least, there is no mention of any assistance), it's a bit unfair to actually show Thranduil and his army refuse to help. By the time he found out there was an attack at all, it would have been days or weeks after the fact.
My Opinion: As minor as the changes in the order of Smaug's attack was (fighting the dwarves outside the gate instead of inside, etc.), I was kind of disappointed in the absence of the steam from the rivers of Dale. It was just a small, cool detail that would have made things more visually interesting - though, honestly, seeing the little bits and pieces of Smaug, itself, was good enough.
You can almost make out his butthole through the smoke.
Including the Arkenstone, as well as Thror's intense greed, are also welcome additions at this point in the story. I don't like things being introduced late in the story and being told how important they are. Setting up the Arkenstone as an immensely valuable stone now prevents some eye-rolling later. Also, Thror is a bearer of one of the Seven Dwarven Rings, and his greed is certainly a byproduct of that. Showing the audience that side of him (and the rings) now is a nice touch.
Thranduil's inclusion sits fine with me, too. As unfair a portrayal as it may be, it cuts down on centuries of history between dwarves and elves and gives a good explanation to the layman, who isn't interested in reading the Silmarillion or all the appendices. Thranduil's refusal to help was never explicitly mentioned in the books, but, neither was any mention made of any offer of assistance. That's conspicuous in itself, and I don't think Peter Jackson took too many liberties in portraying Thorin as bitter about the lack of help.
