The first thing you might notice is about Evernote's new iOS app (version 7.3.0, if you are scoring at home) is that the New Note buttons have been moved to the top. There are still five of them, although the old quick-note button that let you create a list of checkbox items has been replaced by a simple Text button. (You still have the option within a note to create bullet-point, numbered, and checkbox lists.)
Above the row of New Note buttons is a new Settings button. In settings, tap the "Customize home screen" button to access Evernote's new customization options. You can choose one of three color themes: classic green, light, or dark. Next, you can customize the way your various Sections are displayed on your home screen. You can hide or unhide sections, and you can drag them to reorder them. Below, in the Show Details section, you can choose which of the Sections on your home screen are important enough to show a few lines of details (that is, two or three of the most recently viewed notes within each section).
Lastly, at the bottom is a toggle switch for "Show sync status." With this setting turned on, a line appears on the home screen between the Settings button and the New Note buttons that tells you when your last sync occurred.
Evernote also states that it in addition to the usual bug eradication, it has made the app "snappier and more responsive." After using it this morning, I would say that its claim is true.
In related news, SwiftKey Note brings the popular predictive keyboard from Android to the iPhone, along with Evernote integration.