As someone who learned photography "the old way" (film, darkroom, nasty chemicals), there is something to what both of you have to say. My rate of "keepers" in the film days was about 1 shot per roll (1 in 36). My rate of "keepers" in digital is about 1 in 100. So clearly I'm not being as careful to compose the shot perfectly. And I'm definitely taking multiple shots on many occasions with the hope that one will be good.
But my rate of "keepers" per trip has skyrocketed. With film I'd be happy if I managed just 2-3 keepers from a trip. With digital I expect 5+ and am disappointed if I don't get 10. This is because I shoot a lot more pictures with digital
than I ever shot with film. The cost of the professional film I used + developing meant I was paying $0.50-$1 per shot. That put a serious damper on photography. I think the most film I ever shot on a trip was 12 rolls (432 pictures) over 4 weeks, or an average of 15 shots a day. With digital I'll take 2000-3000 shots on a similar trip, or 70-110 shots a day.
FWIW, the rate of keepers seems to be consistent (between 1 in 50 to 1 in 100) among both amateurs and professionals. i.e. The pro photographers aren't getting those great shots by snapping a few pictures. National Geographic did an article on how they make articles. The photographer shot over 5000 photos (on film!) to arrive at the 8 photos used in the article.
Which approach is better? Hard to tell. Though truth be told, equipment actually doesn't matter. National Geographic photographers have intentionally gone on trips equipped with nothing more than an iPhone and still take stunning photos using nothing more than the default camera app.
Equipment does matter. Photography isn't just a matter of seeing something cool and snapping a picture of it. Wide-angles can give you unusual perspectives. Better equipment gives you access to different capabilities. Telephotos allow you to compress perspective, as well as pick out distant subjects without having to run all over. A wider aperture lens can blur the backgrounds more in portraits. Flash exposure compensation can allow you to use a flash, but make the picture look like it was shot without a flash. Zooming during the exposure followed by a flash can create an impressionistic effect which emphasizes the subject. etc.
I recently drove some European friends to San Francisco. Unfortunately we arrived right around dusk, and they weren't able to get a decent shot of themselves with the Golden Gate Bridge in the background. I simply borrowed one of their DSLRs, mounted it on a tripod, put it in aperture priority mode, turned the flash on with FEC dialed to about -1.0, and told them to stand perfectly still for a few seconds. When you do that, the DSLR automatically adjusts the exposure time for the background, but exposes the foreground by modulating the flash. The result was a perfect image of the bridge and city lights in the background, with my friends perfectly exposed in the foreground.
That was GP's point - that better equipment gives you access to more options and different things you can do to take different and better pictures. While it's certainly possible to take good photos with a smartphone, the number of different types of good photos you can take is considerably less than with a DSLR and good lenses. OP misinterpreted GP's post as a film vs digital thing.