It depends on the application for which the file format is being used. If the usage is for planning the manufacturing and process planning the additive manufacturing format is useful . At the Concept generation, concept evaluation and concept selection stages the 3D manufacturing format may be useful to check manufacturing feasibility.
For me both are equal with respect to the function set. AMF was originally an initiative from the ISO and has become an ISO standard in 2011. It is my belief that as always with standards companies want to be different because of commercial reasons. So a new format 3MF was created with companies like Microsoft, Autodesk, HP, ... backing it up. I believe it is supported by default in Windows 10.
The AMF format (ISO/ASTM 52915:2016) is generally technology-independent whereas the 3mf format, generated by a consortium including service providers, software development companies and machine manufacturers at this stage is perhaps more system specific - although of course, with acceptance and adoption of the 3mf format the non-consortium manufacturers of AM systems will make sure their systems are compatible with the format.