You really want to get a notification for every new tweet?
Twitter's official app spares you that pain and keeps it to DM's and mentions (I think mentions). I would be getting notifications every few minutes or seconds even at some times of the day. That's just me.
As some here may know, I own around 30 twitter apps. My fav is TwitBird Pro. Lots of them have built in push notifications, but not one works as well as Boxcar.
I really like Seesmic. And OMG coming from the BB client of it to the iphone one is AMAZING!! Although i must admit, i did like it better on the android. It almost seems like seesmic caters more to android. I may be off base, but it just works really well on there..
I love Twitter apps too! I have different favorites than you guys, maybe because I don't tweet much. I love Brizzly for reading, Trickle for watching a scroll- (like when Jeff tweets live during Survivor!) and Scopy is the coolest thing for looking at all the tweeted pics without having to take all the steps to view them.