Neither game had a great storyline imo. Black Ops 2 is a little better in my book for adding the ability to customize your loadout before a mission, and to unlock more guns by completing challenges. It made it have a very multiplayer feel. So overall I'd say that the campaign in 2 is better. Also I like modern games because vintage firearms bother me, so Black Ops 2 wins in that regard as well.
I like BO1 levels more, but the multiple paths, customization, and challenges are big pluses for BO2. The only thing I disliked about BO2 campaign is that it's too short. I also hated making the arguably most important decision to shoot who.