For a variety of reasons, of course. No the system didn't coast to success on the strength of Pokemon, a series that didn't even get a true 3DS release until 2 and a half years after its launch... just in time for its third Holiday.
I think this question ought to be divided into three -- the first is "Why is Nintendo winning the handheld war in Japan?"
To answer that, why wouldn't they be? Mario Kart on its first Holiday, Animal Crossing for its second, Pokemon for its third, a new Monster Hunter every year, and those are just the really big games. They also had a Dragon Quest remake every year, multiple Mario games every year (natch), and that freak phenomenon known as Yokai Watch. On the hardware side, each iteration represented a significant upgrade over the previous model, encouraging double-dipping (this goes for every region, disregarding the 2DS which only released in the West).
The second question is, "Why is Sony losing the handheld war in the West?" because it's obvious that the Vita was not 'defeated' by the 3DS. Sony's failure is their own doing.
The third question is, "Is Nintendo really winning the handheld war in the West?" Of course they're not. Check the platform totals page. I'm sure it's inaccurate, but surely the numbers are at least vaguely in the ballpark of reality. GBA sales in NA + Europe: >60 million. 3DS sales in NA + Europe: <30 million. Although the GBA technically wasn't fully discontinued until 7 years after its launch, I think we can all agree that the lion's share of its sales came in its first four years, and that the 3DS absolutely doesn't have anywhere near 30 million sales left in its tank, not even globally much less in the West alone. In the end it will barely sell more than half as much hardware as the GBA. That's not a victory, it's a MAJOR flop and we need to talk about it.