I believe that your question can only be answered after taking into consideration the other equipment that either the support or assault kits give you. One of the main strengths of the support kit is its ability to give you reliable information of nearby infantry threats - be it through the handheld scanner, or, more importantly, the IDS-1 infantry sonar. Coupled with an IDS-1 and plenty of cover (i.e. buildings) and corners, the support shotgun can be absolutely devastating since you'll be able to see everyone coming. However, given these criteria, there are many limitations to its use:

- Like someone said earlier, it's probably better to use it while attacking or defending CQC areas
- Obviously do not use on larger, open maps
- Use on smaller, built-up maps like Camp G. or Tunis Harbour. Moreover, on these maps, only use the shotgun in areas in which machine guns would not have a distance advantage. For instance, you shouldn't really use it outside of Toll Station on Camp G., but around Central Camp is fine. Another example is Cerbere Landing - the entire area between South Town Center and Roadblock is acceptable, but virtually everywhere else you'll be overmatched by MGs.
- Enemy titan + IDS = overkill. I really wish more people would do this.

Anyways, I guess my main point is that your equipment determined by your kit selection is as important as your primary weapon, as it very often complements it. You could always choose the Herzog shotgun addon on assault if you really want the "best of both worlds", but you'll find that it'll only be operating at peak efficiency when your situational awareness is supplemented by radar scans on the minimap. This is why the support kit can be so deadly - its technology often enables players to "choose their battles" instead of rushing in or depending on the scans from other people.

I guess my answers to your question probably seem very intuitive, but if you remember just one part of my post, please remember to always place an IDS-1 when using the shotgun!