Sony's handheld device is called the PlayStation Vita, $200. It has better graphics than Nintendo and is a good choice for someone who already has a PlayStation gaming system, as it works as a sidekick to those consoles. So especially with the PlayStation 4, it has remote capabilities, which means that you can play some of your PS 4 titles on your PlayStation Vita.
Nintendo's lineup is generally better for kids because it offers more kid-friendly games. They include popular series such as Mario Brothers and Legend of Zelda. There are three Nintendo devices available: the 2DS, the 3DS, and the 3DS XL, ranging in price from $150 to $200.
The 3DS and 3DS XL do the exact same thing. They both play the same 3DS games in 3D, and they're backward compatible with Nintendo's previous-generation DS games. The only difference is that the 3DS XL is larger than the 3DS.
The 2DS looks a little different but plays all the same games, though not in 3D. Consumer Reports says it's a great choice for any small gamers on your gift list and, at $150, is the least expensive.
Games for those devices cost about $50 each. It's possible to get used games for less. Check online at Amazon and eBay. You can also try stores such as GameStop and Best Buy, both of which offer used video games at a discount.