I use OneNote at work, and Evernote for my personal use.
If you are an MS Office user, OneNote is very convenient. It integrates nicely all the way around the Office apps, and I love the screenshot mechanism that is bundled with it. If you're a heavy Outlook Tasks user, there's some very nice integration with OneNote.
On the downside, OneNote is Microsoft only, there is no easy access from non-Windows platforms. Certainly we have none at work - very useful on my work desktop, and that's all it is good for in my world.
Evernote is fully available everywhere. I access my notebooks with web browsers from windows and linux platforms, with a native app I have installed on some windows machines, from iOS and Android devices. They all sync nicely together, I have the same data available no matter what platform I'm using at the moment.
Moving documents into Evernote is somewhat more trouble on Windows than in OneNote. There's ways to do it, but "Send to OneNote" they aren't...
On the other hand, Evernote's ability to make text embedded in graphics searchable is terrific, and OneNote has nothing comparable. Evernote's "personal" use in my case wanders into work when I embed photographs of whiteboard discussions into an EverNote entry, just so I can search for the words we wrote on the board.
There are a lot more places where one could compare the two. Which one is "better" will depend on your needs - they both work for similar (but not exactly the same) use cases. EverNote is free up to a certain data usage, give it a try. (Caveat: I use the EverNote pro plan, a bit more fully featured than the free version I started with)
For me, OneNote is a convenient tool to use with my colleagues at work, but I use EverNote much more heavily. OneNote is nice, EverNote is essential for my productivity.