I suppose PlayStation used to go more head-to-head with Nintendo in the sense that they had more IPs that were cartoony or family-friendly (or both). But they've been trying to differentiate themselves from Nintendo from the beginning. Their large amount of T and M-rated games is not something Nintendo would do.
They've become less and less like Nintendo it seems over time, but I don't think they were ever trying to create similar experiences.
Lifetime Sales Predictions
Switch: 144 million (was 73, then 96, then 113 million, then 125 million)
PS5: 105 million Xbox Series S/X: 60 million
PS4: 120 mil (was 100 then 130 million, then 122 million) Xbox One: 51 mil (was 50 then 55 mil)
3DS: 75.5 mil (was 73, then 77 million)
"Let go your earthly tether, enter the void, empty and become wind." - Guru Laghima