Userbase is important, but itself can't explain such an outstanding difference so I tried to think some reasons:

1) First of course is the high quality of games. As much as this point is completely subject and down to preference the fact is Nintendo games are enjoying a pretty good word of mouth. This extends to a larger community and the multiplayer experience and is a major point of selling games such as Splatoon, Smash, Animal Crossing and Mario Kart. Anecdotal evidence: I just bought MK8 today (and I never liked the franchise at all) only because I want to enjoy the multiplayer with friends, and if I get bored I can just sell it for almost the same price lol

2) When Nintendo dominated gaming market (NES and SNES) their IPs branding weren't anywhere near as big as today. NES and SNES were build not only with Mario and Zelda, but with huge third party support that put out many iconic titles. The Nintendo effort cultivating their IPs made their fans loyal and (almost) always ready for a Nintendo console

3) There was a point that some huge franchises have their fandom split into handheld and console platforms, with Pokemon and Animal Crossing fans having a huge presence in handheld market while Zelda and Smash had a major presence in consoles. Now every fan of every IP has the same device, and they can try IPs they never have played before

4) Wii, the only huge console Nintendo had after SNES, didn't appeal traditional gamers interested in traditional gaming experiences. The top 10 of best selling Wii games was filled with party and sports games played with motion controls and whatnot, with only Mario platformers and Smash Bros among ""traditional"" games. Switch user base shares a somewhat similar gaming interest of PS4 and XBOX owners, making them much more prone to buy less famous IPs like Splatoon or Luigi's Mansion. To some extent, same can be said about DS, with many of their owners interested in playing Brain Age of Nintendogs rather than more "hardcore" games.

5) Over saturation of formulaic games in PS4 and XBOX consoles. This must be the most polemic point, but I think public might be tired of playing 10 years of the same style of AAA games Sony and Microsoft put out every years. Nintendo games have a refreshing bright design and focus mostly on gameplay and not graphics or story. While people still in love with Sony/MS games they probably find refreshing to find that Nintendo still making funny Mario 3D platformers. The biggest example I can imagine from this type of concept is Splatoon, it offers a TPS experience totally apart from other games on the market

Discuss 

I'd say 3 is the biggest factor. I'd question 5 though. Are traditional games on PS4 doing worse?  Doesn't seem that way to me. I feel like games are generally selling more.

Honestly only Pokemon and Mario, which ironically aren't enjoying exactly new heights in popularity (maybe re-peak for Mario) 

I also think this is too much a simplistic reason, you're essentially stating that Nintendo is blessed with a never ending bright future and no matter what happened they will rebouce just because 

I don't know, their games don't seem to have any legs whatsoever while Nintendo games are chart toppers for years.

TLOU2 has fell out of Top 10 charts in many countries while MK8, Animal Crossing, BotW, etc are still in Top 10 charts months/years after their release.

GoT seems to be doing well so that is a good thing for them.  I honestly don't think a vast majority of PS4 owners care about the Exclusives at all.  This always open the door for a company with refreshing and good games to eat into their market share (see Xbox 360/Wii era).  If Microsoft would have had a better announcement of the Xbox One I think we would be looking at a much different gaming landscape (forced Kinect, Always Online, game locking, etc).

As for why Nintendo games are selling so well, good games have good legs is the easiest way I would sum it up. 

We had this same exact thread topic a few days ago?

Why are Nintendo games selling better than they ever on the Switch?

https://gamrconnect.vgchartz.com/thread/243040/why-are-nintendo-games-selling-better-than-they-ever-on-the-switch/1/#3

Is it my turn to make this thread next week?

Sony games have never had the same sales pattern as Nintendo games. That's not a new thing this gen. It really doesn't have anything to do with the question of whether Nintendo games are selling better because gamers are getting tired of what's available on PS4/XBox One.

I'm a Disney fan and I get your point. Each of their comeback status (late 80's and early 10's) had more complex reasons than what you are stating nonetheless. They came from reorganizing the way they designed, marketed and sold their movies

Of course for some franchises their status and cultural impact, their branding, will remain mostly unbothered, so anyone with proper resources and a good strategy can make them work again. But this need a business model that works in first place

What I want to discuss on this thread is what is the business model or growth strategy they are using to make the brand hot again. In case of Nintendo, what is behind the surge in sales of their IPs? Why are getting new peaks?

Since the other thread fizzled out quickly, and this one posits some possible explanations to chew over, I think it's ok. (Unless the rest of the mod team disagrees and decides to lock.)

Oh, now I know where the idea for this thread comes from lol

Sorry, but if you believe in Jung functions then you will forgive, I'm a Ni-dominant person 

You don't have 8-year-olds showing goofy white parents charts to buy Bayonetta 2 on TV.

The switch has interesting hardware. It's not aimed at grandmas or 8-year-old Bayonetta fans or whatever the fuck those family time ads were. It's marketed well and aimed at young adults and teens for the most part in marketing. Oh, and the games just seem better versions of those IPs. Where Switch has New Horizons. Wii U had Amiibo Festival. Xenoblade X the black sheep of the series (tho I love it) where Switch has 2, Torna, and DE. 3D world to Odyssey (I like both but c'mon of course SMO wins) Where Nintendo published Ninja Gaiden 3 on Wii U, We have Astral Chain on Switch. Better hardware. Marketing and better versions of those games and just better games.