Controller: Give you that one, they sucked harder than a vietnamese prostitute. In the seventies :P
Vibration pack: Oh come ON. Nintendo introduced vibrating controllers to the console market (for PC "Force Feedback" had been available for a loooooong time). Then Sony improved it (Rumble released April 1997, Dual Shock released November 30th 1997 - 6 months after Nintendo).
One analog stick: Nintendo introduced the concept to consoles and gamepads. Before there had been joysticks but never on a controller like this. Yeah, compared to PS1 Dual Analog (and later Dual Shock) it sucked, but do remember that Nintendo had developed this already in 1995 (though the console itself turned up 1996), and Sony had the Dual Analog ready a whole year after that - well into the lifetime of the PS1, so it wasn't on every PS1 the way the N64 controller was.
Cooling: Never happened to my N64, despite having it on for 24-hour marathons of DK64. Might've been a problem with your specific unit or a specific game? Not saying it didn't happen, just that it probably wasn't a general fault.
Cartridges: Aye, they crap out when kids do that, but it's not NEARLY as bad as scratched discs. You seen the kids' DVD collection at your average family? Yeah, they would have been equally scratched in your family.
From what I remember the N64 was more powerful hardware-wise but suffered from the cartridge memory restrictions and the fact that it was hard to develop for and therefore max the performance. When you had the option of having a buttload of textures and CD-quality music on the PS1 vs few-and-compressed textures and synthesized music on the N64, the choice was rather clear. It got better with the GameCube, but 1.5GB vs 4GB again turned out to be a really painful limitation...