First of all, in the Discover menu, everything is now condensed — tweets, activity, people Twitter thinks you should follow are in one stream. Search has also streamlined so you view tweets, photos and accounts in one place.
On the iPhone front, there’s now a search button (a little magnifying glass), which already existed on the iPad and Android apps, but is new to the Apple phone. In the connect tab, it’s now easier to change what you see — new followers, just interactions, retweets, whatever — right within that section.
Also when you click links now, Twitter takes you straight to that URL rather than just expanding the tweet. Overall, it’s an update that makes sense now that we have access to it. [Google Play, iTunes via Twitter]