Twitter has plenty of meta-discussion. (TODO: It would be interesting to approximate the percentage of tweets that are about Twitter.) Very frequently (at least among the people I follow) the discussion is about iPhone apps for Twitter. More often than any other, I see people recommend Tweetie. Though Twitterrific is mentioned frequently, and I see TwitterFon come up increasingly often.
I use Tweetie and Twitterrific Premium. The contrast between the two is interesting. They're both excellent, well-polished apps that illustrate two different approaches to designing a quality iPhone application.
I use Tweetie often enough that it gets a spot on my main launcher screen (reserved for the apps I use more frequently). It's full-featured. In fact, it seems like I can do just about anything in Tweetie that I can do from twitter.com.
But I use Twitterrific more often than any other iPhone app, so it gets the privileged spot on the bottom left (on the strip on the bottom that appears on all launcher screens). Twitterrfic is a good example of the "do one thing only and do it well" school. Twitterrific's one thing is reading tweets. It does that so well that I prefer it to twitter.com on my MacBook Pro (though I haven't tried any desktop Twitter apps).
Twitterrific Premium's killer feature (which I haven't seen or heard of in any other iPhone Twitter app) is how it "maintain[s] a reading position between launches of the application". (I think this feature is not in the free version of Twitterrific.) This is why Twitterrific is my most used iPhone app. I can very quickly launch is and scan through all the new tweets since the last time I checked.
As I'm reading in Twitterrific, if I see a tweet with a URL that looks interesting that I want to take the time to look at later (especially if I don't want to take the time to wait on EDGE), I'll mark it as a favorite.
Then later (when I'm on WiFi on my iPhone or my MBP), I'll use Tweetie (or twitter.com) to scan through my favorites and un-mark them after I read them.
I also use Tweetie occasionally to check for replies.
And Tweetie is better for writing tweets, especially if I want to include someone's name or a URL. And the new version 1.2 has an optional landscape keyboard.
Loren Brichter updates Tweetie much more frequently than Craig Hockenberry updates Twitterrific. But that is expected when you think about it, since there is always plenty of opportunities for new features and improvements to a full-featured app like Tweetie, whereas Twitterrific is so specialized and so polished that @chockenberry should be very careful not to fix something that isn't broken. But if @atebits adds a "maintain reading position" feature to Tweetie that works reasonable well, I may give up using Twitterrific and give Tweetie the place of honor on my iPhone.
But when/if that happens, I won't regret the $10 I spent on Twitterrific Premium. I use both often enough and both are so pleasant to use that the $10 and the $3 for Tweetie was money well spent. I recommend both.
Update: I remembered one more situation where Tweetie comes in handy. Twitterrific has a limit on the number of tweets it will hold, so if I can't make time to check it for a while, or if the number of tweets is much greater than usual for some reason (such as the inauguration), then when I come back to Twitterrific I'll notice that the "last read" tweet is at the bottom of the list and I won't remember reading it. In Tweetie's advanced settings I've changed the "Initial Load" to 100 (from the default of 20), so I can catch up on missed tweets often by just opening Tweetie and scrolling down (or maybe touching "Load more..." a single time). Yes, I know that Twitter isn't email, and I don't feel the need to read every single tweet that goes by, but if I've just missed an hour or two's worth, Tweetie makes it easy to read them.