And what is this egregious limitation to which I refer? Why, it's the simple task of creating a new notebook or even a new section. You can edit OneNote notebooks that you've created on a Windows PC or tablet until your heart's content, but you can't create new notebooks with the iPad app. And on existing notebooks, you can't even add a new section; you can only add new pages to an existing section in an existing notebook. Until this basic functionality is offered in OneNote, iPad users are better off paying for the $14.99.
With the bad news out of the way, allow me to walk you through some of the improvements this update offers. For starters, the app is free (for a "limited time") and removes the previous limit of 500 notes before it hit you up with a $14.99 in-app charge.
Also, OneNote now boasts a consistent design across all devices (well, minus create new notebook and section buttons on the iPad app). The previous skeuomorphic design that mimicked a spiral notebook has been replaced. Now, the page you are working on is given more room on the screen, with the navigation panel more narrow and moved to the right edge of the screen. Need more room to operate? Then tap the arrows in the upper-right corner to go full-screen. Also, Microsoft Office users will find a familiar ribbon across the top of the screen, which offers a host of rich-formatting options. The previous version was plain text only.
Next to the full-screen button is a search button that searches for your keyword in the title or anywhere on the page, though you have to be viewing a notebook in order to see the search bar to search all notebooks. Wouldn't it make more sense for the search bar to be accessible from OneNote's home screen?
The app lets you view inking for handwritten notes or diagrams you may have made using the full Windows app -- or Outline+ -- but the app doesn't support inking should you feel the sudden need to scribble something on your iPad using OneNote.
You have two options to sync your notebooks across your various devices running OneNote: SharePoint and SkyDrive. You can sign into each by tapping on your account in the upper-left corner of the home screen and choosing Add a Service from the Connected Services section. Multiple users can edit a synced notebook simultaneously. Also from the home screen, a new Recent button sits along the left edge, which conveniently lets you access notebooks you've been working on recently.
One last note before you update OneNote on your iPad: Microsoft states, "Upgrading users should sync their existing application data before upgrading."