I finished the available parts of the Alliance war campaign. There are three "chapters" available, out of four total. I'm somewhat surprised that Blizzard didn't time-gate each chapter. It would have fit well, and each chapter is a reasonable chunk of content.
The first chapter is working with Jaina to fend off an assault on Anglepoint. This was a pretty good use of a previous location and NPCs. Also, the final cutscene combined with the Achievement name ([Kul Tirans Don't Look At Explosions]) was very amusing.
The second chapter was this very odd blend of comedy and tragedy, where you use a gnomish device to "embiggen" an intelligent gorilla at the cost of his intelligence. The gorilla volunteers for this operation, seeking to strike back at the Horde (goblins, naturally) for hunting his people. So the entire quest line is a bunch of things that are normally funny, but kind of aren't anymore. I'm not certain if this was a good idea or not, but it was an interesting way of presenting the usual light and mindless gnomish shenanigans.
The third chapter was a treasury heist scenario featuring our favourite Alliance rogues, Mathias Shaw and Flynn Fairwind. Even though they're both rogues, they're both very different characters. Lots of fun banter. The scenario itself was pretty interesting, with several traps that you have to navigate.
I believe the second and third chapters are setting up potential bosses in the Dazalor raid.
There's still one more chapter, which I'm guessing unlocks tomorrow.
All in all, the Alliance War Campaign is pretty good. One interesting thing Blizzard is doing this expansion is taking their time with the story. 8.0 was all about setting initial outposts, and trying to avoid the enemy's attention. In 8.1 things are heating up, and there is more direct confrontation. This long view of the story is interesting, especially as we see many complaints that the factions aren't clashing as much as people think they should be.
Edit: One thing I forgot that I wanted to point out was that Blizzard was very good with cutscenes featuring your character in this patch. The aforementioned first chapter cutscene with both your character and Jaina walking away from the explosion was particularly stylish.