Tweetbot is my twitter app of choice from Tapbots. I only use twitter with my phone, as the similarity to texting suits the way I derive benefit from the service. I think of it much like texting "the world" in a sense. I don't use multiple accounts or have particular need for any advanced analysis and reporting tools (for which there are some excellent apps). All I need is Twitter's basic functionality and I want it presented in the best possible way.
Tweetbot has a custom interface, which looks incredible while being familiar and intuitive. Its beautifully animated and the gesture interaction is excellent. It's suite of custom sounds are simple and understated and immediately identifiable. Push notification support was recently added (but I was quite happy without it) and it has excellent predictive @mention and #hashtag support. It's visually superior to most of it's competitors, though is functionally similar to the official Twitter app. It's easily worth the asking price if you're looking for an alternative and enjoy apps with a particular appreciation for aesthetic and ergonomic quality.