I'm not sure why I haven't given Echofon a serious try before this (think I first gave it a spin back when I was on an Android handset, so it wasn't particularly useful then), but I suspect it's going to become my primary Twitter client.
I was previously using TweetDeck for Chrome and the Android phone, which allowed me to keep track of things pretty conveniently. But after getting an iPad and switching to an iPhone, I've found it to be pretty annoying having to figure out which updates I've read and which I haven't.
(Plus, TweetDeck doesn't seem to keep track of Facebook updates as well these days, making it less useful than it once was.)
Echofon syncs the unread tweets between clients (whether tablet, phone or computer), which is exactly what I needed. I think that the paid desktop clients are ridiculously priced (US$10), so I'm happy to stick with the ad-supported free versions for now, but am starting to think I might just fork out the US$5 for the ad-free iOS version after all.