In general you should have property placeholders defined in your symbol for those properties you want on the parts, a placeholder is a property but without an assigned value. Using placeholders ensures the information is in the correct location when it gets added to the part during placement or packaging. Typically it would be REFDES or # (pin number), Value, Tolerance etc.
DEVICE is usually defined on the symbol as it is the unique identifier used in layout (in conjunction with PKG_TYPE) unless you can share symbols across parts, so in this case you will need to duplicate the information in both the database and on the symbol. The information in the database is usually considered 'parametric' something that defines the part without affecting it's packaging in the PCB, typically Value, Rating and tolerance. In the end it is up to the user to decide what makes sense as purely additional information that doesn't affect packaging and what uniquely defines a part and needs to be embedded in the symbol definition (pin swap information for example would not come from the database). Finally, the user needs to decide how much information a symbol needs to have attached to it for the purposes of design and manufacture.