I have just started using onenote, so far its awesome, however it seriously lacks deep browser integration and cross platform features of evernote.
I agree that OneNote isn't integrated cross platform as well as Evernote. Especially when it comes to browser embedding. Hopefully it will get better but I think the gap isn't as big as it used to be and it's no longer a big enough gap to make me second guess my decision to no longer use both but to be 'all in' with OneNote.
Here's a list of cross platform uses for OneNote that you may or may not be aware of.
Mac- MS office is on Mac
Iphone/Ipad- I've been told the OneNote app is pretty great on these, especially the iPad. MobileNotr is a good 3rd party app for it.
Android- Just came from Android, MS's official app as well as MobileNotr are on there. Worked ok but I wished I could make shortcuts to notes. Nope, have to open the app and navigate to your note every time. Evernote is way better on 'droid'.
Web- Skydrive app version is very good
Browser Integration- Obviously Internet Explorer has great integration, though I think there are 3rd party plugins for Firefox and Chrome that give you 'send to OneNote' functionality.
Evernote has had a syncing advantage for years. The reason that it's the same everywhere is because it has very simple formatting so a web browser version of it is pretty much the exact same capability and use experience as their desktop version. So they started with the lowest common denominator and spread it around. Not trying to be insulting, I like E-note and think it's awesome. But if you compare the two desktop versions, it's night and day difference. Like how excel is so much more powerful than the gdocs spreadsheet app. For some people's use, that difference doesn't matter. If you are making a grocery list, then the difference doesn't matter? but if I'm taking lecture notes or tying together a big project then I want to do that in OneNote.
MS had to take a powerful and elegant best-in-class note application and try to make it accessible via browser and mobile. E-note built theirs from the opposite direction. Only now has MS started to get sync and ubiquity 'right'. Evernote still does some things better but the sync and ubiquity advantage has almost disappeared to where the only E-Note advantage is a vast user base and 3rd party developer support. That is still a huge difference but I hope it starts to change in the same way that I hope WinPhone becomes a solid #3 in the smartphone world.