As @twitter as platform has grown the capabilities of it's service hasn't evolved with it. As such there are so many annoyances and difficulties in using @twitter.
Filtering Tweets: @twitter supports muting or blocking users for spam. But can't hide same tweet retweeted by multiple users. And no standard way to filter conversation involving 'others'. Two chatty people can pretty much fill the TL.
Not suited for discussion: Though one-to-one conversation works fine, it can get messy when involving more than few people. Facebook/Google+ are better suited for discussion rather than @twitter.
Too Casual: When @twitter decided not to sync unread tweets it was clear the focus of the platform is to be casual messaging network and not being an serious social network. And so @twitter will never be an replacement for Facebook or Google+. And with every day @twitter becomes an media and news discovery network connecting random people. Problem is there are other sites like Reddit which works better for discovering new stuff than @twitter.
As such only use of @twitter is casual rant/whine as and when required from mobile rather than of any use. With @twitter wanting to monetize the service at the earliest and the flaws which are by design, it's unlikely anything will change in near future.
tl;dr - @twitter doesn't serves any purpose for me