PS1, PS2, Wii, GameBoy, DS, 3DS. Outsold the competition despite the competition's greater power.

yeah, but the difference is that those platforms were able to run games, not as good, but they played them, wii/wii u missied on almost 98% of the great games on ps3/360 because they couldn't even run them, and it will be the same with switch, you will NEVER see red dead redemption 2 on switch, you will NEVER see mass effect andromeda on switch, etc.

N64 was stronger overall, but not in every way. Each had advantages over the other. PS1 could do higher resolution textures due to more texture cache and the larger storage capacity of CDs. 

On the other hand, N64 had more RAM (4MB standard or 8MB with the expansion pack versus 3MB in PS1) and more modern features like trilinear filtering, perspective correct texturing, and anti-aliasing.

One of the major differentiating factors was that the PS1 hardware was a very efficient and easy to develop for, while N64 was by comparison quite convoluted and difficult to get optimal performance out of.

Yeah, that's kinda my point. Was it really though? REALLY? IN PRACTICE? NOT JUST ON PAPER!!!!???? lol. Excuse me. Very gassy. Third party crossover titles were not that numerous. Sometimes clearly better on one than the other. Sometimes a tossup. And yes, both the hardware, and software medium created a complex stew of differing results. Too much to effectively get into outside an actual mouth-to-ear convo. My rub is this: N64 was a tech letdown. That ad Onion posted? That was the foundation of the entire buildup towards the system. There has never been anything like it. Not before. Not since. Maaaybe the PS2. But that was several years later. Hyperbole, and yes, lies, were easier to see through by then. I wish I still had my old EGM's and Next Generation magazines. It was going to be so much better. Until it really, mostly, wasn't. And to beat the same drum: I find this to be a contentious topic, but on VGC, people all say the N64 is the tech god-king of gen 5, and everybody just scratches their privates, rolls over, and goes back to sleep. I thought this was Playstation country! :)

In practice, I would still say yes. N64 games visibly used techniques like perspective correct texturing, anti-aliasing, and trilinear filtering to produce results that avoided a lot of the visual flaws common to PS1 titles like pixelation and texture/polygon warping.

Now, that's NOT to say PS1 was weak. It was a powerhouse for its time and could rival and even best N64 in some ways despite releasing 2 years earlier. It's kind of like PS2 and Gamecube, where each wins in some areas, one has the overall lead, but that doesn't mean the other is a slouch.

Nintendo's bragging about N64's power wasn't really much different from, say, Sony bragging about PS3's power.

For about a year, the n64 was a beast. I think, according to EGM, they even won on sales. Unfortunately for them, expensive cartridges (for consumers and developers), size limitations, and being difficult to optimize killed any power advantages they had. Not to mention Sony's ability to add controller features to ps1 very quickly.