I have been asked this question a few times recently, so I thought that I would write a post. I have tried a few apps and will tell you which I settled on and why. This list applies to both iPhone and Android with a slight exception in Tweetdeck which you will see below.
1. Hootsuite: Hootsuite for Mobile is as full featured as the web client. You can access multiple Twitter accounts, schedule tweets, view your Facebook stream, and send one message to multiple places at one time. I have not had any problems with the client crashing, etc. like I have with others. It is clean, easy to use, and reliable. The only thing that I do not like is that it does not have a way to auto shrink tweets. But then, neither does the desktop client. The Hootsuite app does not notify (PUSH) on iOS, but it does on Android.
2. Tweetdeck: Tweetdeck was my favorite for a long time. It is still a great client on the iPhone. It includes an easy way to bring up a list of your follows while composes a tweet, insert a hashtag, or shrink a link. My favorite feature here is the ability to swipe to the next screen, or column. I do not like Tweetdeck on Android at all. It is not as clean or easy to use as the iPhone version. And the interface looks flat and as appealing to the eye.
3. Twitter: The official Twitter app is a great app. The interface is clean and easy to use. Although it does not quite keep up with the ease of the columns in Hootsuite and Tweetdeck, you can still easily save searches and lists for easy access. The Twitter app only lets you access one account unlike Tweetdeck and Hootsuite though. Probably the best feature of all, the official Twitter app notifies you immediately of new @ mentions and DMs via PUSH.
4. Seesmic: Seesmic has added some interesting features since I last checked it out. Most notably the addition of “spaces” on the home screen. This gives you easy access to more than on Twitter account, a Facebook stream and even Ping.fm info. Other than that the interface is pretty simple and does not offer many bells and whistles over a standard Twitter client.
So which do I use? On my iPhone I use a combination of the official Twitter app and Hootsuite. Why both? Well because as mentioned above, the Twitter app does PUSH alerts, so as long as I am logged in there I get alerted to new messages on my main Twitter account. But, when I am actually browsing Twitter or creating my own Tweets, I prefer to do so via Hootsuite. On my Evo (Android) I exclusively use Hootsuite which does alert me to new messages and mentions.
I suggest that you try out a couple and choose based on what feels right for you. Some prefer the more simple interface of the Twitter app, while others need to do more advanced functions like scheduling tweets or accessing more than one Twitter account.
Which is your favorite?