I suppose much of individual perception has to do with what generation a given individual is from and how long they have been actively following the industry, presumably as a consumer rather than as a casual observer.
I would argue that by the late 90s, the Playstation brand had eclipsed Nintendo as a gaming icon in terms of market relevance. Certainly by the 00s with the rise of the PS2, the Playstation brand was cemented as the default brand in gaming. However, Nintendo has more iconic internally created IPs than Playstation due to differences in how each company approached brand building.
For Nintendo, their brand was synonymous with their IPs and the characters that made them. That is strong branding considering that some of their most popular IPs date back to the 80s (Mario, Metroid, Zelda).
By contrast, the Playstation brand has new IPs with each generation that largely define a given generation's console software library. IPs that remain relevant over two hardware generations are rare exceptions in contrast to Nintendo's approach to each generation gets a new version of previously existing Nintendo IPs with omissions being the rare exception.