I've used a number of different applications to manage my twitter streams. I started out using Tweetdeck, but at the time it couldn't accommodate multiple accounts. It also had some other issues, which I know annoyed me at the time but seem inconsequential now. I tried a few different twitter clients including the web application of peoplebrowser. This had a lot of potential and I went on to try the air application of peoplebrowser.
For one reason or another I kept going back to Tweetdeck. Then one day I discovered Seesmic Desktop, another air application. At first I didn't like Seesmic because it lacked a bunch of things I liked about Tweetdeck. As I used Seesmic more and more I liked it more.
1. The user lists are great. Put users into a list to track them in a separate stream.
2. The searches are saved and you can have them appear in your home stream or not.
3. Multiple accounts are easy to manipulate and use with Seesmic (I currently am managing 3 twitter accounts and a facebook acct from the client)
4. Your streams get color coded so you can easily see what messages are replies, DMs, or messages posted by you.
5. You can set the application to notify you with a sound when a reply comes in (you can notify with sounds for other posts but then my computer would be beeping of the hook!)
6. Seesmic now has integrated bit.ly account information. This way you can enter the pertinent information into your setting and anytime you shorten a link it automatically sends it to your bitly account. This type of integration is true for 5 other services as well.
7. The new Beta also has autocomplete of user names - an excellent addition.
On the down side I really, really miss 4 things about tweetdeck.
1. I really liked being able to tell which tweets I had read and which I hadn't. This is not available in Seesmic unless you empty each stream once the tweets are read (you can't mark them as read) (this is available in the new version of Seesmic web)
2. The ability to click on a twitpic link and have it show up in a popup window was really nice. Seesmic opens a browser window. (inline viewing of pics and movies available in seesmic web app)
3. The way you could click on a person to get their profile was implemented better in Tweetdeck.
4. The way in which you create groups and add members to groups is nicely done in Seesmic, but the checklist method implemented in Tweetdeck is better.
If Seesmic implements the ability to check and work with following/followers lists, then I would never have to use the twitter website again.