On Linux? Do yourself a favor and try Hotot.
I've used a lot of twitter clients over the years, I even wrote one back in '08. TweetDeck is pretty good, but Air is shoddy on 64-bit Linux, and so it didn't integrate well and would crash.
I rejected Gwibber and Choqok, just not my style. My old web standby Brizzly seems pretty lame these days too. Then I found Hotot. It's awesome. It's like a Linux native TweetDeck, but with a friendlier, more welcoming feel.
If you are looking for a Linux twitter client, you have got to give Hotot a try.