I downloaded TweetBot, but I still think Twitter for iPhone is the best twitter app. Twitter for iPhone is faster, has push notifications, a very clean UI, shows the number of tweets a user has, among other things. Also, it has a very nice feature where you can swipe the top left icon to return to your timeline no matter where you are. This is a nice feature because at times you look at one person's profile and then from there another and so on. Then to go back to your timeline on other apps you have to click the back button a bunch of times. Also, TweetBot has positioned the Accounts button in the upper left hand corner which I accidentally press often as it's in the same position as the back button. Kind of annoying.
Tweetbot is a very attractive app, but it doesn't do anything more than Twitter for iPhone. I think it received more praise than it deserves because Tapbots is known for making very usable and attractive apps, which it does, but I don't think the functionality matches the design.