All the S Notes are saved as “snb” files (a zip container) in both devices. You can export them to “pdf” or “jpg” but they will not longer be editable.
Now, when you create or edit a S Note on the 10.1 (the “snb” file is created or gets updated on the 10.1) the hand drawings on the S Note are no longer editable on the 5.3. You can see them, but if you try to edit the note they just disappear (images, figures and text boxes do not have this problem).
Finally, if you do not need the S-Pen precision at all, the infinity should be a better option.