I remember coming after a heated Genesis/SNES war, there was little friction between the two. I'm wondering why there wasn't a full scale war.
My guess would be that they both targeted different demographics. N64 was for younger people who would become core gamers. PS1 seemed like it was a console for more casual adults who wanted to play a little NHL or something. And the two bases had real little reason to war with each other.
Whereas Sega vs. Nintendo in the 90's and PS3/PS4/X360/PS3 now are all going after the same demographics.