One of the biggest differences between the novels and the anime is that you get Kirito's thought process in the books, which obviously explains a lot more as to his motivations and actions. Some of the game systems are covered in more depth in the novels as well.

Event-wise, the differences worth pointing out in the first half:
* Episode 2 comes from a side-story (Aria in the Starless Night) and they cut out a ton of stuff - scenes with Kirito meeting Asuna for the first time, scenes with Argo the Rat, a bit of mystery with someone wanting to buy Kirito's weapon, more scenes with Asuna and Argo
* The blacksmith girl's side story is from her perspective and has some extra wrap-up from when the game is cleared that was cut.
* The murder mystery episode (based on volume 8 - A murder case in the area) plays out a bit differently. They go more in depth into the various systems of the game, Kirito and Asuna do more detective work, there are scenes with Kirito and Asuna discussing the murder with Heathcliff and asking him questions. The scenes were completely cut from the anime because they give away who he is to the reader even though Kirito and Asuna don't know what's up at the time.
* The final battle in Aincrad makes more sense overall, since it is clear what is happening, unlike in the anime where they visualize Kirito imagining himself dying.

For the second half, there are only a few differences I remember:
* A big side event where Kirito and Lyfa explore an underground dungeon is skipped entirely. It is important for some of the side stories, like Caliber.
* In the battle against the angels to enter the tree, when Kirito gets Lyfa's sword, he actually dual wields and chops them up, instead of some absurd charging attack that doesn't make any sense.
*After Kirito fights the guy in the real world, he doesn't just leave him there without doing anything.

That said, if you wanted to continue reading straight from Volume 5, you wouldn't be missing much.