The only one I've used at all is the Twitter app.
And the jury is still out.
If I'm doing any tweeting, chances are I'm using my phone.
Among its advantages - it was the first available option for 'quotable retweets' - the retweets where you add something to the front and then 'quote tweet' rather than straight up retweeting. So I'm in the habit of doing that only from my phone. (And to be honest, I don't even know if you can do that from the computer yet.)
I just find the iPhone app easier to use overall. (At some point I'll explore TweetDeck or other Twitter apps. I know there are other options out there than the plain old Twitter app.)
But I like the Twitter computer app too. It's easy to write tweets from, it does a great job of quickly pulling up mentions (like if I type in @ and then some letters the options come up), and I like how it changes the text color for hashtags.
But it's not perfect - It's not obvious to me when there are new tweets on my feed, and I don't like that you have to use the 'File' menu at the top of the screen for so much. It seems so five years ago. And I admit some of these problems are my own fault - I am not used to checking it constantly, like I am with my phone, so sometimes I forget about it and lose sight of new tweets.
This is a pretty New Thing - I'm writing about it too soon to pass real judgment. I'm sure, though, as spring (and baseball season) approach and I'm on the computer a lot watching baseball and keeping tabs on the Twitter feed, I'll be using the app quite often.