Yeah but that's a Nintendo handheld.

Because Nintendo on its hand helds has those amazing titles that really move units.

A new Pokemon, Monster Hunter, Mario and now Yokai have legs that can cancel out dozens of titles on a competitor's system.

Everyone has been begging for a full on home console Pokemon, but Nintendo knows that a lot of us (myself included) bought a 3DS in large part because that is where we get our Pokemon fix.

Sorry, but for who say "one word = Pokémon"... and the around 35 million 3DS before X and Y how was sold!? :|

That's because the 3DS is great and the PS4 is great. They both are awesome and should both be given the same amount respect and both should be placed on a throne, since they are considered as the royal family.

As members of the royal family they also have less royal but still noble friends ( The Xbox One )

Then there are the WII U and the PSVita both are jesters which while they provide even more entertainment then their noble counterparts, they unfortunaley have never been able to garner as much respect and cash.

Both 3DS and Vita got impacted by the smartphone tsunami. However Nintendo's "house" has a better foundation, so their house wasn't as badly damaged, whereas Vita's house got completely destroyed in the storm.

Nintendo still has the kids market, Nintendo loyalists, and the Japanese market to lean on for the 3DS, plus they had a good 1st holiday season for the machine which established an ok working base for the system going forward.

Also taking Monster Hunter away from Sony was like kicking someone in the balls when they're already down. That's the proverbial straw that broke the Vita's back. That's probably the smartest single thing Iwata has done in the last 5 years. 

Which wasn't doing very well until Nintendo dropped the price by 32% within 5 months of release.

You also have to account for pedigree.  Nintendo has always produced good, reliable hardware with good software output.  With Smart phones eroding the casually interested that swelled the market last gen and disposable income being limited, it was inevitable that Nintendo's reliability would win big points with those still committed to dedicated hardware.  

GBA had 3 years before the DS was released to succeed it, 3DS will need 6 years probably to get to 80 million at this rate (I'm not even sure if it ever will to be honest). 

This is like saying "well we both finished a 1 KM race, so we're both equal" ... yeah ... not if I finished it in half the time you did. 

But the market is split now, wasn't then.  And disposable income is not as abundant for most people.  Just saying, you have a bad habit of taking numbers in a vacuum.

Because the Vita sucks kidding

I think it's because of the strength of their IP's, mainly Pokemon.