Twitter is better than Reddit because it is decentralizes the information from single, topic-related feeds people can post to, to one feed per person that you can subscribe to. This makes it much faster and more convenient than Reddit for getting status posts on things you like, i.e. an independent game developer's latest WIP.

Some people have split accounts that you can choose to follow to receive different kind of status updates from them, so an example of this is a person with a 'oh look this interesting thing happened in my life' account, and a separate account for 'oh jeez I'm really angry and need to vent about this to a subset of people I know in relative privacy'. Because of the nature of twitter it feels easier to throw away or make lots of accounts than, say, facebok.

The real connection comes not when you follow celebrities, but when you're a creator (Or a budding creator), and you interact with other people who are creating things for support or advice; or you have an interest in what your friends are posting and doing, and like viewing their traveling posts and their reactions to things. If you have those sorts of relationships twitter helps facilitate them extremely well, and if you don't, or the people you interact with in that way don't use twitter, then it won't have that value for you.