I use the first two you mention (APP and PixInSIght) as my main stacking programs. The reason I use two is I owned (because I hate renting stuff) APP before I got into PixInSIght. I run two imaging cameras (Color and Mono) and select the camera I want to use for the Moon stage. As mentioned in another thread my Color camera is super sensitive to stray light (ie. Moon). The other consideration (even though my old eyes can't see it) is a Mono camera is said to give a higher resolution in the images. The use of filters with a mono camera can enhance the visual perspective you want to achieve.
Back to stacking. I use APP for stacking my Color camera data. The main reason for me is I don't have to mess around and debayer the color images like I do in Pix. I recently discovered just how well the APP mosaic tools work. Easy, efficient and great results. For my mono data I use Weighted Batch Pre Processing (WBPP). Some will argue this is the lazy way to do it, it is "Batch" prcessing which won't get you as good a result and individually calibrated...... Say that if you are doing it with 60 hours of data....
Anyone who has started AP in the last 7-8 years is familiar with DSS, RegiStax, Gimp, AutoStackert and many more. The are familiar because that is all they had. Depending on what you image Deep Space, Solar, Planetary.... can influence not only the Capture program but also the processing.
Just however is just my opinion.......