Synchronizing S-Note notes between S4 and Note 10.1 2014
I have seen a similar issue trying to sync S Note's between a Galaxy Note 3 (smartphone) and a Galaxy Note 10.1 (as well as to a Galaxy Note 2).

The issue seems to be in the version of S Note running on Android 4.3.

On my Note 3, S Note saves the files as .spd files in a Snotedata folder.  On the Galaxy 10.1 the S Note documents are as .snb files in the "S Note" folder.

I think this explains why sync isn't working.