Owner of both and quite honestly, my 3DS is currently hidden somewhere in a dark corner while my Vita has been getting tons of playtime, the 3DS is a fantastic system by all means, its got a fantastic amount of great exclusives but I just find it so severely lacking in everything else. Only reason I'd personally recommend it is if you truly, truly love the exclusive franchises on it.
The Vita just looks and plays so much better for me, the second analog stick is a godsend and the things some of the developers already did with its hardware is pretty darn impressive, like how utterly huge Gravity Rush's world is for a portable game or how Killzone Mercenary offers a surprisingly great console shooter experience. The ever growing amount of indie games combined with its gigantic backlog of PS1\PSP classics and ports will also ensure that you'll always have something to play. That remote play functionality with the PS4 is also bananas, and it works as a second remote too saving you some money in the long run (although an actual second remote is better, I'll admit).
Sorry if this sounds so one sided, ultimately the best I can recommend you do is hit up Metacritic, check out the top games for both (and delve a bit into the games a-z list there) and just chalk up the total amount of games you'd absolutely love to play on both devices and compare the numbers, the one with the most games you'd love to play being the obvious choice here.