Here's why:

• It supports push notification between Twitbird users
• The interface is clean and very fast
• It supports groups
• There's a reference to the original tweet in replies
• It includes a link shortener (bit.ly) and three image upload services (TwitPic, yFrog and Mobypicture)
• Landscape mode works everywhere
• You can save links for later reading or email them without exiting the application
• The only drawback so far for me is the looking of the user interface but this will be addressed in v1.2 with custom background support

I'm using it for two weeks now and so far I'm very happy with it. It's the most complete Twitter client for the iPhone I've used to date. The Pro version is not free, but it's worth the money. There's also a Lite version available free of charge, that doesn't include multiple accounts, push, translate and read later features.