Quests are one of the strong points of the game. There are no boring MMO style Collect X Rabbit paws or whatever BS. First, there is a main, central plot to the game that I've found interesting so far. It involves the Daedra trying to invade all of Tamriel. Then there are the three faction storylines. I'm only involved in my own character's faction quest line so far, but what I've liked about it is that just about all of the quests in the entire zone have been related to the ongoing faction storyline somehow. It connects everything and makes the world seem whole and interconnected. All of the quests I've come across have been fully voice acted as well. And they seemed to have hired more voice actors since Skyrim, which I thought suffered from the same 5 or 6 voice actors doing all of the characters. They even got the guy who played Dumbledore in Harry Potter to do the main quest line NPC.
Also, the various guilds have their own story/quest lines like in Skyrim. My favorites have been the Thieves Guild and Dark Brotherhood which IMO have better stories than their Skyrim counterparts. There's also a new guild called the Undaunted that focus on having you kill tough monsters in dungeons.
I feel like the main difference between Skyrim and ES:O is in the combat. The game has typical MMO style skill based combat where you learn skills, put them on a hotbar and use them in combat. Combat is very much run up to monsters and whittle them down with your skills, healing every now and then. One thing I miss from Skyrim is being able to play a stealthy, archery based character. There are bows and there is sneaking, but I haven't seen any way to combine them into a build yet.