How to interpret various thermal-related filament properties?
This depends on application.
Definitions:
Vicat softening point. Vicat softening temperature or Vicat hardness is the determination of the softening point for materials that have no definite melting point, such as plastics. It is taken as the temperature at which the specimen is penetrated to a depth of 1 mm by a flat-ended needle with a 1 mm² circular or square cross-section. [However, it seems force on needle should be included.]
The heat deflection temperature (HDT) or heat distortion temperature (HDT, HDTUL, or DTUL) is the temperature at which a polymer or plastic sample deforms under a specified load. This property of a given plastic material is applied in many aspects of product design, engineering and manufacture of products using thermoplastic components. [Again, to be meaningful, the forces need to be specified.]
Basically, Vicat softening temperature involves ability to be cut, while heat deflection temperature involves distortion from an evenly distributed force. Thus, use the parameters based on whether sharp uneven forces or a distributed force is most important to your application. This can also be worded Vicat is for maintaining shape, HDT is for maintaining load bearing properties. In other words, Vicat is for uneven loading on the print, which can change the shape. The most extreme is a sharp load. HDT is for the print to support an evenly distributed load.  Many applications may be in between the two.  What complicates the issue is 3D prints are ususally printed with a fill rather than being printed solid.
Appendix
Standards to determine Vicat softening point include ASTM D 1525 and ISO 306, which are largely equivalent.
The heat distortion temperature is determined by the following test procedure outlined in ASTM D648. The test specimen is loaded in three-point bending in the edgewise direction. The outer fiber stress used for testing is either 0.455 MPa or 1.82 MPa, and the temperature is increased at 2 °C/min until the specimen deflects 0.25 mm. This is similar to the test procedure defined in the ISO 75 standard.
Limitations that are associated with the determination of the HDT is that the sample is not thermally isotropic and, in thick samples in particular, will contain a temperature gradient. The HDT of a particular material can also be very sensitive to stress experienced by the component which is dependent on the component’s dimensions. The selected deflection of 0.25 mm (which is 0.2 % additional strain) is selected arbitrarily and has no particular physical significance.