Same reason PlayStations winning the console war.

Strongest brand for its sector.

(And because you don't consider the mobile market handheld gamers)

Nintendo builds their handhelds to appeal to the young crowd. 

When kids see a 3DS and a Vita, they would be confused to what a Vita is. A Vita is built sleek and sexy and designed for the pro gamers. When a kid sees a 3DS, it intrigues them, it looks super fun and they will cry if you don't get it for them. It has become the new cool toy. Parents and grandparents eventually get pulled into playing 3DSes because kids can't beat some levels and want them to play the hard parts for them. Thus an ecosystem has been created.

Also cool boyfriends buy 3DSes for their cute new girlfriends. They want to create bonding moments with them and this is a means to do so. This leads to trust and love. The boyfriend is eventually able to get some. Innocent touching turns into full blown sex. Babies are created and we are back to the beginning of the cycle.

Make kids love it, that is how Nintendo wins.

There's barely any competition when it comes to the portable market of gaming.

That, and Nintendo handhelds have healthy libraries of games, including Pokémon.

Its mainly the price.

The Vita launched waaaay to expensive, because they made a monster of a handheld.... which wasnt needed, they should have designed a cheaper handheld, that was just abit faster than the 3DS, but sellable at simular prices.

also as some have said... handhelds need to be really kid friendly, to become mainstream.

Most vita owners are probably late teens - adults... while most 3DS owners are probably kids.

Pokemon.

Also, it sells to kids.

1. mobile is winning
2. because nintendo made first party games for it. since third parties are ignoring 3ds/vita for mobile 3ds is the only one with any games.

Nintendo has a bunch of multi-million selling franchises, Mario platformers/spinoffs, Pokemon mainline/spinoff, Animal Crossing, Smash Bros, Mario Kart, Zelda, Nintendogs, Kirby, Donkey Kong along with big hitters in Japan like Monster Hunter, Yokai Watch, Dragon Quest.

I was going to say the same thing...
It's hard to say "winning" when they've sold 50 Millions 3DS, when there are 7 BILLIONS mobile phones around.

Sales of 3DS are also poor nowadays, when compared to the DS.
My opinion is that the NX will be some sort of smartphone which will both be able to play dedicated Nintendo games, and Android games.

That said, they probably still generate many profits, because at least people PAY for the games. (unlike the awful free-to-play model that clutters the mobile gaming world)

Nintendo games just have that special magic that makes you all tingly inside, and makes your dick hard.

Nintendo pumps out so many 1st party games on their handheld that it hurts their Wii U development, where as Sony clearly supports the ps4 MUCH MUCH more than the Vita. Sales for the 3ds are MUCH higher than the Vita and ps4 sales are higher than the Wii U's.