For me, it's mostly the one-to-many follower scheme (which Facebook emulated, but poorly), and the fact that it's used by so many media personalities to directly broadcast to and interact with their audience. I find it much easier to get an impression of what opinions are out there about stories as they break on Twitter than on Facebook, because the opinions are in my feed rather than associated with some article about a relevant topic (and also because they're shorter, it's easier to consume a lot of them). Also, some journalists break news on Twitter without writing an article, which means I can get new info there before it's even been reported on the news outlets.
Twitter isn't a particularly good platform and I hope someone builds something better soon. But it's still, in my opinion, superior to any of the alternative social media platforms (which isn't saying much about my estimation of any of them) if you're trying to get a diverse array of opinions/perspectives on news stories in real time as they unfold.