I just go ahead with my standard cast-on in situations like that. The backwards loop one is going to create less of a ridge on the inside since there’s less yarn involved, but I don’t like it. I find it difficult to knit the next row and to pick up stitches from later.
With specific techniques, the designer might just be following what they’ve always been told to do or they might have tested a bunch of ideas and decided this one was the best for the particular situation. I will often include something in the pattern notes if I chose something out of the ordinary/specific to share why. I tend to just tell you to cast-on, increase, etc. without telling you specifically how so you can pick your own method as often the specific method doesn’t matter too much.