I've been noodling away on a review of Twitter clients for the iPad, but Viticci did a great job. Read his instead.
Clark seems to like the official client. For me, I've stopped using the official client because I no longer trust Twitter's design sense. I've been using TweetCaster Pro on the iPad for basic twitter use. I like the simple conversation and attachment view. On the iPhone I use Tweetbot.1
But when I'm researching something using Twitter, there's no beating TweetLibrary. It's the power user app. Unfortunately, it is a little rough around the edges. It's slower than other apps and crashes occasionally. BUT, it handles search and collecting tweets better than any other app I've tried. For example, published tweet collections. Viticci is exactly right. TweetLibrary is rethinking what Twitter is for.
I wish they would make a native iPad app. ↩