Is there some difference between the data protection level or encryption strength of the Private and Public levels?
There is absolutely no difference between the Private and Public levels in terms of the application security or encryption strength (AES256) of the stored data. What differentiates the two levels is only their respective data sets (i.e. files and folders), which are kept strictly confidential and restricted to each access level. It is only the user that decides how/when to access the Private and Public levels and what to store at each level.