I have to go with Wii, for the power of Xenoblade and Pandora's Tower alone. But Wii Sports and Sports Resort were also great games. So this overall makes Wii the winner.

Otherwise I would go with Gamecube, as it introduced Pikmin and Luigi's Mansion.

According to the Nintendo online store the Pandora's Tower copyright is owned by both Ganbarion and Nintendo and The Last Story is owned by Mistwalker and Nntendo.
It seems to be the same situation that Nintendo has with Koei Tecmo, in which they both own half of the Fatal Frame franchise. Nintendo learned this approach from long time Nintendo partner Owe Bergsten who only ever buys 50% of a company so that they can be on equal terms rather than one ruling the other.
The rest is owned by Nintendo.

https://www.dualshockers.com/nintendo-last-story-wii-trademark/

Right. Nintendos website mentioned the copyright being shared with Mistwalker. I failed to state that fact.
Their store never mentions trademarks, which is perfectly normal.

So in the end, Nin still has the trademarks of those ips.

Some additional franchises that I thought of:

SNES: Yoshi's Island (Yoshi's Story, Woolly World, Crafted World series)
N64: Pokemon Snap (N64, Switch), Pokemon Stadium (Coliseum)
Wii U: Super Mario Maker (this and Splatoon were major innovation from Nintendo, imo, during the Wii U era)

From a commercial success perspective, Pokemon has really been Nintendo's biggest new-IP find since the NES days. While this started on a handheld, the N64 was really the first home console that saw Pokemon games and it did get a lot of them and so I will give N64 the Pokemon prize for the purposes of this thread. Smash Bros is probably #3 on the list for new IPs in terms of popularity post-NES after Pokemon and Mario Kart and so I will have to say that the N64 is the overall winner here.

It's a tough question though because the SNES had so many franchises that started on the NES but rose to fame in a major way on the SNES (Mother, Final Fantasy, Metroid), it just seems unfair to give all the glory to the NES for these franchises.

Wii U

Only reducing the Wii U to Splatoon really ain't cutting it, there are tons more:

• Super Mario Maker
• NES Remix
• Tokio Mirage Sessions
• Nintendoland
• The Wonderful 101 (at the time Nintendo still owned the IP)
• Hyrule Warriors (if it counts?)

This, especially the bolded part. Funny thing is, I like Smash more than I do Kart (because the only ones in the MK series I really enjoyed are the original and then a looooong way to MK8), but I voted SNES based on reach and importance of the series rather than my personal taste in this case. 

I had to give my vote to the SNES for how amazing Mario Kart, Donkey Kong Country, F-Zero, and the early Starfox games are.

The only new N64 franchise I like is Sin & Punishment, and only Gamecube one I like is Luigi's Mansion. No new IP on Switch has really done it for me so far. Freaking love Xenoblade and The Last Story though, and Wii Sports felt downright futuristic back in the day, so Wii takes the #2 spot for me.

That's a tough one, as there are at least 1-3 I love from each gen. Overall, though, I'd had to go SNES. Mario Kart, DKC, are two of my favorite series, and still love the original F-Zero as well as GX on Cube.