First, Sony brought to market a system that was disc-based from the very start. That was an enormous leap forward. You only need to look at Final Fantasy VII to see that. Should Sony get credit for FF VII? Probably not, but we're talking about perception.
Second, in contrast to Nintendo, Sony supported and promoted third-party content. They put it front-and-center and used it to appeal to people who were getting weary of Mario and the limited amount of content you could get from cartridges. This is something we still see today, with Sony running ads for third-party games while Nintendo only advertises their own stuff. Even if Nintendo and Sony had all the same games, the image they seek to create has been different. In all honesty, that's something I fault Nintendo for as much as I credit Sony.
Yes, that's just perception, but it played a huge role with the fourth and fifth generations.
Sony, with the PS2, also decided to stop making consoles look like toys and they added in and promoted media features. Those were smart decisions on their part. That went a long way toward breaking the perception that gaming was only for children.
