Hootsuite [$1.99 on sale until Dec. 17 - iTunes link] is a hybrid client that not only provides basic Twitter functionality but also hooks into Hootsuite's own services to provide statistics (on things like ow.ly click-throughs) and scheduled tweets (so you can set it to tweet "Happy New Year!" while you're busy getting your champagne on).
In our brief tests, it offered good functionality especially for a first release, with an interesting take on many of the standards, and if you have (or are willing to create) a Hootsuite account as well, it brings a host of new features to the table.
(Though no, push notifications isn't one of them yet).
If you give it a try, let us know what you think (especially you, Bla1ze!). More screens after the break!