According to Strategemini's review on the Anniversary Edition page, emphasis and formatting mine:
What has been removed?
Articles. There are no more Pathfinder Journals. Many of the articles that were in the adventure path were also removed. All articles on Gods (Desna and Lamashtu) have been removed. The history of Karzoug was removed. The culture of the Stone Giants was removed. The History of Thassilon was severely curtailed. So what remains of the articles? All the location articles are preserved and updated. Sandpoint, Magnimar, Turtleback Ferry, and Xin-Shalast all have their own articles. The "Magic Of Thassilon" article is preserved and expanded (though "More magic of Thassilon" is removed) in the form of "New Rules". The new Rules article has updated versions of spells, items, and a new mechanic for tracking Sin and Virtue Points in the campaign. Finally all the introductions to the various APs are removed.
Some Bestiary monsters have been removed, but they were either optional to the AP (like the Sandpoint Devil and the Attic Whisperer) or they are now in one of the published Bestiaries (and thus easily referenced from the PRD). Other than certain Bestiary monsters there has been no in game content that was removed. Every encounter is there, every dungeon is there, every important NPC has a statblock.
What has changed?
Almost all of the earlier art. Mostly for the better. Ameiko Kajitsu and Shalelu Andosana both reuse Art from Jade Regent, but there's new art for the goblins, the Skinsaw Man, Aldern Foxglove, the handouts (such as the deed in the Skinsaw massacres and the letter in Sins of the Saviors), as well as Belor Hemlock and Orik Vancaskerkin. Some art (like Aldern Foxglove, Korvus the Goblin, and the Skinsaw Man) is an incredible improvement. Some art (like Vancaskerkin's new portrait and Belor Hemlock) is slightly disappointing. On the whole though the new art is a boon.
The stat blocks have also changed, some have merely been updated to pathfinder mostly verbatim with third party classes preserve,(e.g. Delphine's entire encounter in module 5) and some have been completely overhauled (e.g. the quasit in module one is now a Witch instead of the Thaumaturgist she was in the original iteration of the path). Additionally, the final encounter with the big bad of the adventure path has been heavily overhauled with an entirely new map, new stat blocks, round by round instructions, and additional hazards and participants.
In addition to everything being updated, there are several new monsters in the Bestiary like the Scarlet Walker. There are New Magic Items like the Anathema Archive. Additionally Several merely magical Items have been updated to Artifacts.
But the biggest addition is in the campaign itself. There are far more connections between and the modules now. You meet Ameiko Kajitsu's father in a fairly interesting encounter early on in Burnt offerings, for instance, among many other small additional encounters throughout the book. There's an entirely new Dungeon section (for sloth) in the Runeforge. That's in addition to all the changes and the new Items discussed earlier.