Who makes the best handheld gaming system (Nintendo or Sony) and why?

i would go with sony ..

PS vita is like the ps3's left boob

Nintendo.

although it has become less appealing throughout recent times, it still has a better library and history.

Nintendo, did it first and does it best (Though Advertised as a "Handheld" system the Virtual Boy not withstanding). Sony always falls short, specially with wasting their time with the PS Vita which is the PSP V.2 that nobody actually wanted nor gave a damn about.

Its really all up to you. Sony's ps vita will be best for fps and all around has a good overall design and build to it. To me, library is lacking a lot. I dont have one by the way. Also it is very expensive due to the memory cards you would need to buy and the console is just more expensive in general.

3ds is my console of choice. If you haven't purchased one but are thinking about it, GET THE XL!! regular 3ds has so many poor design choices, such as screen scratching (get screen protectors) stylus placement (not a deal breaker though) and my biggest pet peeve, it has a freaking glossy finish ON THE INSIDE OF IT!!! the most fingerprint magnetic gaming device ever!! Get the xl... But as for the library, 3ds is freaking amazing!! We have great retail games like monster hunter 3 ultimate, etrian odyssey 4 (my favorite 3ds game and 3rd fave game ever) and soon to get a zelda lttp inspired game!! Can't freaking wait!! Also has amazing eshop games like mutant mudds and the denpa men.

Go for vita if you want
1. First person shooter games
2. Better build quality
3. A decent battery life

3ds for
1. Okay build quality
2. Amazing games of all genres
3. If you will be near your charger often
4. Much cheaper then vita overall