Nah it was when they were releasing nothing for 2 years. Just a 2 year drought.

That definitely tanked sales and let water into the boat, but once they put their first party games on PS the boat flipped over.

I'm pretty sure GameCube was the only time Nintendo bragged about specs, and look how that turned out. When they started giving details about GameCube, they bragged about the superior specs to Dreamcast and PS2.

I don't think they bragged about the specs of SNES and N64 compared to the competition, but somebody can correct me if they did. 

The N64 was literally named for its hardware specs and they would talk about leapfrogging everyone else by a generation by skipping the 32-bit era and going straight to 64-bit.  The Gamecube bragging was tame by comparison.

With the SNES they liked to play up Mode 7 in the marketing and then of course when the SuperFX chip was developed that was a big deal marketing-wise with Star Fox and Donkey Kong County.

Look... No.
You are repeating some dogmas, implanted in the media by some people, for too long. And they are FALSE:

Saturn... I don't know in US, but for sure was selling better than PSX in Europe and Japan by the end of 1995 and during most part of 1996, so no way.
Why? cause PSX had crappy exclusives franchises, apart from Ridge Racer, in 1995.

In Saturn, in 1995, you had Sega Rally, Virtua FIghter (original and Remix), Virtua Cop, Daytona USA (and, please, don't tell me "it was a crappy conversion" THAT early port in Saturn was amazing and fun as hell and fantastic for everyone who got it or could play it. Even today it's fun as hell. It's bad fame was totally astroturfed), Panzer Dragoon, both Clockwork Knight 1 and 2, International Victory Goal (that was probably the best soccer game by then, in a console. Not joking) and even Virtua Fighter 2 (january 1996 in Europe).

Many gamers in Europe and Japan prefered BY FAR a Saturn in 1995 than a PSX, no need to trust me if you don't, but it was like this, sorry.
And NO, nobody knew about that 100$ E3 crap there, until 20 years later, thanks to some Youtube video. In Japan, by the way, both consoles were already in the market since 1994, and Saturn was selling better: How that "100$ comment" in 1995, could even do an influence there? 

Instead, PSX in 1995 had Ridge Racer, Toshinden (and people totally forget about Toshinden by 1999 or even before), the very first Wipeout, Destruction Derby 1, Tekken 1 (Tekken 1 was NOT as famous and loved as Virtua Fighter series by then) and... things like "Kileak the Blood" (yes, that was "an important title") or Jumping Flash (another title many PSX users doesn't even known... 3 years later). BUT, Wipeout and Toshinden... were also launched in Saturn some months later (as soon as early 1996 in Europe for Wipeout, and late 1995 in Japan for Toshinden). And even Destruction Derby was launched in Saturn in 1996 in Japan and Europe. Not even those games were exclusive for PSX.
Playstation was a very weak machine in 1995 and part of 1996 in catalogue. Also, it had no RPGs, at least in western countries, until 1997.

I'm not saying PSX was worse as a console. It wasn't. I'm saying Saturn was much desired by gamers cause its titles and exclusivities in 1995 and even 1996. Even the very first Tomb Raider (a PSX classic series, by many) was launched some weeks earlier for Saturn in 1996.

All that crap about "the 100 dollars and the famous E3 speech of Sony's guy" is an American BS exaggeration. Don't extrapolate that to Europe and Japan, because you'll be wrong: yes Sega America could do some things wrong in the 90s, but the real problem for Saturn, worldwide, was not that "speech", but the GIANT and COLOSSAL importance Sony had by then as a conglomerate, in many industries, and they used all its influences they alredy had in the music and TV/film industry, and in the big megastores (as an appliance manufacturer), to sell the PSX. They used everything they could and buyed all the adds and sponsorships they can in the media (magazines, radio, TV channels...) and in the top sports events during many years (for example: being "Playstation" the "UEFA Champions League" main sponsorship during some years, the most important soccer competition in Europe). Everything to sell its console, as well as buying many third party exclusives starting by 1997 or even 1996 (Tomb Raider 2, Resident Evil 2...).
And they eventually succeeded. Sega did not had all that money and influence. Neither Nintendo by then, btw.
So... They did the very same thing Sony fanboys accuse Microsoft to do it now against them, but much more openly agressive.

Of course, by 1997 everything started to change in favour of PSX, because ALL of that. Sega just could not compete. Maybe by then, also, some Sega America's CEO made things even worse and THAT also affected Europe. OK. But not because "that random guy" in may 1995 telling US americans a 100$ discount since day 1 in PSX US launch.

And about N64. N64 had a PHENOMENAL Holiday 1997. All 1997 and 1998 were just AMAZING in N64... I can hardly understand why are you talking about the 1997 holiday. Yes, FFVII was a spectacular game and huge success for PSX, and most probably was the moment PSX boosted its sales and put itself as the winner, good for Sony. That had to be expected, after 3 years in the market with huge financial support, some great games had to come. Gran Turismo, by itself... yes, it sold a lot, but Crash, Spyro, Tomb Raider series and MGS were also very important for PSX. And all of them, started to come in late 1996. Not before.
But N64 also had LOTS of great games during all those 2 years (now, very classic ones, and not only OoT or other Nintendo games, but Rare, Acclaim, Konami ones...), and sold very well in US. Not that well in Japan, were Saturn sold better caused by a continuos and better support from Sega Japan until 2000. Sega America started to abandon Saturn already in 1997. 
N64 suffered a lot because the original idea of restrict third party presence in the N64 searching for "quality", the price difference caused by cart technology, and in some markets, the HUGE piracy PSX had (and that was totally decisive to understand the final PSX numbers, apart from the huge amounts of money Sony put into its promotion during the first years, and some time later, buying exclusives)

GCN suffered from not having DVD player in 2001, being launched way too late in PAL markets (mainly Europe, mid-2002), and not having the GTA series when 3D GTA games arrived. Basically.
Also, its name, shape and purple color promoted as the "main" color... were not so popular in 2001: People (broadly) started to like GC 15-20 years later.
The machine was excellent, but PS2 had total control of the market after being alone in the next-gen market practically one whole year (thanks to Sega's dismissal of Dreamcast in January 2001: Impossible to choose a better timming... to help Sony). So, third parties just ended doing PS2 ports to GC, and after 2-3 years, stopped to do even that. Capcom was the only third who tried hard to support GC the first 3 years (after its none existing support for the N64).
XBox had a similar GC situation, but got a DVD player, and MS spent lots of money to promote it, specially in US. So... it ended to sell more than GC.