Both have their own unique games.
Xbox has the Halo series and Playstation has Little Big Planet.
I'm assuming they want one because their friends have them? I'm also assuming your kids are around the age of 5 - 10?
Since they are wanting an Xbox 1 I'm assuming there is a certain game they want / their friends have. That's why I asked about their age.
Break down - both require an online subscription in order to play the games online.
Both have motion sensing peripherals. Xbox has the Kinect and Playstation has the Eye.
I haven't had the chance to try out the updated Eye but the Kinect has definitely proven itself to be entertaining - especially for the young crowd.
Both have packages available with the without their motion sensing peripherals and you'll notice it mainly due to the price difference.
I think currently you can get a standalone Xbox1 for 349.99 and an Xbox1 W/ Kinect for 449.99
Playstation 4's are running at 399.99.
I'm sure the Holiday Bundles are out by now. They tend to include a game or two as well within each package. With the two being in a similar price range I would recommend getting them the Xbox1 like they requested.
I would definitely check about the games as well because Black Friday has some fairly decent prices going for standalone Xbox1's.
I think
Walmart had a deal for a standalone Xbox1, the Halo collection, and a 30$ gift card for 329.99. Whereas the Xbox1 + Kinect is around 429.99 that weekend.
Feel free to PM me if there was something more specific you were looking for.