Overgeneralizing can be subjective but more or less patterns emerge.
Nintendo fans care about that style of 1st party software that Sony or MS can’t capture. Their games are whimsical, for adults they make you feel like a kid again and recapture that feeling of wonder and fun you had in the younger days. For kids it’s likely the first console they have because their parents had Nintendo or just figure its the most family friendly brand. You don’t play Nintendo for the power and bells and whistles; you play for titles that are unique to gaming and ones you call your friends over to play on the couch.
Xbox and PS fans are simpler. Games that look lifelike over whimsy. We want our consoles and to have the best specs because that means better looking and performing games. Complex narratives with nuanced characters. Mature content (not blood per se but more like adult themes) and quite simply the best 3rd party content.
PS gamers tend to love 3rd person games. “Single player 3rd person story driven action adventure first party” games they can’t seem to get enough of since Sony’s best exclusives follow that formula. I’d say Xbox gamers gravitate more towards some combination of FPS, racing, and WRPGs.