STORY PT. 2
What Black Ops II does very well, better than most of it's contemporaries, is the presentation of it's story (and Black Ops I was pretty good at this too): Most military shooters today choose to go the way of Modern Warfare, presenting the plot via loading screens by hearing dialogue and watching satellite images. The cutscenes in Black Ops II however, are fully rendered and let you see who is talking. This serves as an excellent demonstration of the value in seeing characters emote as they speak about their experiences. Seeing the face of the person talking makes a big difference in keeping you invested in the story. Now, occasionally, you do see a cutscene in games like Medal of Honor or Battlefield 3, but it's usually filled with drab military chatter and there isn't much in terms of story progression. In Black Ops II, the dialogue flows and is understandable without straining your ears and brain too much – this is largely because it's actually somewhat interesting to listen to.
Frank Woods tellin' it like it is during a cutscene
The cutscenes put more emphasis on the characters' motivations and what must be done next, rather than simply presenting mission objectives. The game even makes a few attempts at connecting with you emotionally, though I'm sure it varies from person to person how much it actually accomplishes this. Obviously, it doesn't do it nearly as well as in an RPG or action adventure, but for a military themed shooter, it's doing a decent job.
The biggest innovation to the game's story is that it lets you affect the plot, which isn't something very common in military shooters, and certainly unheard of in Call of Duty. Certain missions and actions during the campaign will affect the ending. There are even branching paths in the game, which obviously add to the replayability. I'm surprised more shooters don't do this, considering how widely adopted player effected storytelling is becoming, and I think it's one of the many things Black Ops II does right. A few open ended missions whose outcome effect the plot also differ quite a lot from the regular missions, so I'll cover them more in the gameplay section.