While I rely heavily on Twitter for Mac (originally Tweetie) on the desktop, my choice on mobile for Android (and Windows Phone 7) has been Seesmic - both due to its intuitive and lengthy feature set, but the constraints put on Twitter's own client.
Twitter has stated (and likely they've done so rightly) that they want to appeal to more of a mainstream audience - one just coming to grips to a 140-character world full of weird languages that contain hashtags, RTs, replies, lists and other oddities. They also have a business premise of promoting their service as the exclusive place for news and social discovery. This has left an opening, taken by both TweetDeck and Seesmic, to provide a client that supports both multiple services and multiple accounts - on both desktop and mobile. For the power user who needs to use multiple accounts, you simply cannot do that on the official Twitter client for Android today, full stop. And forget about using Facebook, Google Buzz, or any other service. It's not their interest. So I've had to shop around.
Since the company's pivot from video comments to major social media client, Seesmic has forged an interesting role of being available on practically every mobile platform and OS, adding Ping.fm for broadcast to multiple services simultaneously, and recently, doubling down on enterprise efforts with early support for Salesforce Chatter and keeping close ties to Microsoft with one-off deployments for the Windows platform.
Seesmic first gained praise from me about 2 years ago with the launch of Seesmic Web, which was much more fully featured than the Twitter alternative. With Twitter having revamped to "#NewTwitter", the gap is less clear, but on mobile, Seesmic still reigns supreme. Having gotten frustrated with slowness, application timeouts and the inability to use more than one account on the official Twitter account, I turned to Seesmic, and the application not only did more, but was faster and extremely stable. No more failed searches and force quits.
Beyond the standard Twitter functionality, from timelines, mentions, profile browsing, saved searches and list support, Seesmic's acquisition of Ping.fm means I can post to multiple accounts across services simultaneously, and the services are more than just "check the box" implementations. I was surprised to see how deeply you could monitor fan pages on Facebook, and the addition of Google Buzz support is welcome for me.
Amusingly, one of the boons of Android also turned out to be a detraction, for after Seesmic's installation, I would not only receive notifications from the native Twitter app that replies and messages were waiting, but the same activity would double down my alerts, coming from Seesmic as well. So I did the unthinkable and the official Twitter app is off my Android devices, which eliminates duplication. Meanwhile, on Windows 7, Seesmic was the first app I downloaded, comfortable the experience would be familiar and very useful.
To paraphrase the fun line of commercials from Dos Equis, I don't always tweet from my mobile device, but when I do, I use Seesmic. If you need multiaccount and multiservice support, it's the best dedicated client for the job. I even told them so myself for an article Wednesday on the company's blog, one of many folks who told Seesmic why they were the choice.
Disclosure: my6sense, where I am VP of Marketing, has an Android client, of course, and our app contains the ability to share updates to Twitter, Facebook and Google Buzz. If you're trying really hard, you could consider Seesmic a competitor. :)