First off, I really enjoyed the campaign, but I do feel like there are a few things that might have made it better.
Storm of Steel: Really good as an intro. Does a good job of showing the pointlessness of WW1, and just how bad it was, without going overboard.
Through Mud and Blood: Similar to Storm of Steel for me in showing the brutality of frontline combat, but is maybe a little less dark in attitude. The MK. V tank looks totally badass as well. I'd almost have preferred that the part where you fly the pigeon was the end though, cos that hit me pretty hard, but that will never do that again.
Friends in High Places: This one was a wee bit disappointing, as much fun as it was. First, the flight controls are completely different to the flight controls in multiplayer, which makes it kinda confusing. Second, I think it would have been really cool to play as the Red Baron, instead of some fictional character. Could have had a bit more history in there, and a view from the other side.
Avanti Savoia: Really liked this one. Having the armour was really cool, but the best bit for me was after you use the AA gun, when you are looking for Matteo. Going down into those trenches, and the tunnels below and seeing the soldiers either dead or curled up crying hits me pretty hard. It tries to show how the war affected people, and the first time I played through this story, I had to move on, else I would have started crying myself.
The Runner: Probably my favourite of the 5. Shows the brutality of the war, while having a few laughs in there as well. Fredrick Bishop is probably my favourite character out of all the characters in the game to be honest. I also just liked the fact that Gallipoli was in there, cos being a Kiwi, I was really hoping to see that, whether I got to play as a Kiwi or not.
Nothing is Written: Comes close to being my favourite alongside The Runner. The open layout and Far Cry-esque missions may not have been groundbreaking, but they were hugely fun for me, and I'll probably play through it a few more times to try different play styles.
TL;DR: I enjoyed the campaign hugely, but, I do think it could have been better with some more historically based stuff, such as playing as the Red Baron, but, it is a BF game, and doing that might have stopped them from giving us a campaign with "Battlefield moments".