I use Evernote on my Note 10.1(older model) and it's synced with my PC and S3. It works just fine with no problems. Just as a word of warning, if you are thinking of using the S-pen to take notes, Evernote does not have pen support. You would be typing all of the notes. You can use Skitch which is made by Evernote, but it is mainly for annotating pictures. Another workaround is a keyboard app that supports handwriting. I've dabbled with a couple of this type of keyboard app and they work okay but I don't think they would function well for long documents or pages of notes.
The tablet does come with S notes which I think can be saved to Evernote, but I don't think the file is editable after it is sent to Evernote(not sure haven't really used s notes).