Using your Microsoft account, OneNote will sync your notebooks and pages across the cloud regardless of the platform your using. And OneNote is on all of them: Android, Windows, OS X, Chrome, Kindle tablets, and the web.
When you want to share a page, you can either share a link or export it as a PDF and email it from directly within OneNote.
Organize everything in notebooks
Instead of forcing you to manage a neverending list of documents, as Notes does, OneNote provides the option to create notebooks. For example, you can have one for work, school, your personal life, and maybe even a daydream notebook.
You can then add pages to each notebook, further organizing content within a category. This makes it even easier to sift and sort through.
It's just better
Microsoft has done a tremendous job with bringing OneNote to Apple products (amongst others). With frequent updates and feature additions, its clear OneNote has the advantage of Apple's Notes. The five features named above only begin to scratch the surface of OneNote's full capabilities.
For example, the Mac app recently gained the ability to record voice notes — hopefully we'll see that feature brought to OneNote for iOS soon.
While there's something to be said about the simplistic approach Apple has taken with Notes, sometimes it's just not enough.
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