Sounds like some people really have no clue as to how and when to down shift, it is not an exercise in destruction. There should be no wear on engine or transmission to speak of. That's why I don't let many drive my vehicles.
Why would there necessarily be pro's and cons? It would just seem to be preferences. Sometimes I do one, then do the other.
You would save a little on brake shoe wear, or wear a little on engine clutch and transmission. Brakes could fail during a stop, and you could just let out the clutch in a lower gear. I have had that happen.
Just as often as having a clutch fail and drive home without one.Had that happen twice.
Pretty much how I do it. Only had 1 clutch in over 110k miles, broke a 2nd gear out of the blue. I have had two 3sp+od transmissions so, being sixty to seventy yo I take great care.