None of the TV type boxes are a rival to a console. In general they allow you to play apps or in-built games. They don't have the capacity for complex graphics and none of the major games will be released for them.
If you are serious about gaming then a PC with decent RAM and dedicated graphics is a good alternative to a console as you can obviously also use that for other things such as browsing the internet, homework/office work etc. Consoles don't have that ability but are cheaper than a decent gaming PC. Games for PC gaming can be purchased as a disk or downloaded via websites such as Steam etc. You can also get Netflix etc via your PC.
That would free up your TV obviously too. The majority of the big games are made available via PC but some have a later release date.
You also (in general) can't sell the games on which you can do with console games.
Consoles are really designed with the only purpose of playing games but all the major consoles now offer blu ray and internet access to netflix, iplayer etc too.
The kinnect is good, but you need a biggish room as you need to be far enough away for it to be able to pick you up. If you already have a wii for interactive type games, I'm not sure I would go for an xbox purely on that point.
The main thing to establish is which type of console their friends are getting. I know that you can chat through xbox live between the 360 and the Xbox one although you cant play games across both platforms - even if it's the same game. I would imagine that is the same for Playstations across PSN.
My experience in the past was that Playstation was better for younger children as there was more variety of games, whether that is still the same I don't know as mine are teenagers now and despite all the consoles, more or less exclusively use their PCs.