Where to put an Xbox One when flying, carry-on or checked luggage?

It should not be a problem to bring it in your cabin luggage.

You should do this, and avoid putting any valuable electronics in checked luggage (where they can easily be stolen).

It is best to put it in carry-on luggage. This is the usual recommendation for anything which is valuable as long as it is permitted by size and is not a prohibited item. The general idea is that anything which can be used as a weapon, used to construct a weapon or mislead people into thinking it is a weapon cannot be taken in carry-on luggage. An Xbox is not on any such list that I know of. It should also fit within carry-on guidelines for most airlines.

Having the item with you lets you to keep a closer eye on it and reduce chances of it being mishandled or stolen. Do pad it properly in case you are asked to check-it gate-side which may happen if space onboard gets full. Usually this is due to limited overhead bin space but you can always mention that it will be placed under the seat in front of you, unless there is not such space because your seat is at the front-end of a plane section.

Though I have transported graphics cards and motherboards in checked luggage I would never trust doing this with a hard drive or a DVD drive where there is big potential for problems to occur due to rough handling.

I see that the xbox one has a flash drive rather than a traditional hard disc so its OK there, however a common problem that arises with many games consoles is that the laser used to read discs gets knocked out of alignment leading to read failure.

I've never travelled with an xbox one but I have taken a PS3 and PS2 with me on planes before. You usually have to take it out as you go through security, just like with a laptop, but it is no issue overall. People know what an xbox is and the x-ray machine will recognise its not a bomb.