Twitter

Compared with Blackboard, Twitter is more open, more casual, and quick to respond to. Since tweets are supposed to be short, it makes people say their main point. Another benefit is in the different ways people can respond, either simply liking a post or retweeting. The biggest part is that it allows those not very confident in speaking to "speak" their mind. 

That does not mean Blackboard has its own advantages. Discussions on Blackboard are far better organized since they are contained within your class, showing threads, the number of replies, total posts, etc. Threads also show replies in chronological order and not necessarily the most liked replies. Since it is on a more educational basis, it's really focused on what you can write. Unlike Twitter, there is no tight character limit so people can be as in-depth as they want. 

In class discussions, while they can be very effective, they can also just go sideways. Many times in class discussions, only a select vocal few contribute and things can get heated where the original point of discussion is lost. Not only that but they're hard to record too. I've had great whole in-class discussions but they are so few far and between.