The Xbox One is the newer console and uses a completely different architecture. As a result of that backwards compatibility is non-existant. It is the same with the new PlayStation which doesn't work with games from the previous model.
Unfortunately gamers on Xbox One (I'm going to refer to it as X1 from this point onwards) cannot play against 360 gamers. They can friend each other and send messages. All a gamer on a 360 would see is an X1 logo next to their friend's avatar when online rather than what they're playing.
The 360 is a good console but is near the end of it's life. Some developers are still developing for it but I see many heading over to the new machine next year. In the case of annual sports games on the 360 FIFA in particular will be a 'legacy edition' starting next year, essentially meaning full price for a roster update rather than new features. They do this now for the old Wii and PS Vita.
Playing online on both cost the same annually but on the 360 the free games given away with Games For Gold each month are yours even if you let the subscription run out. On the X1 your paid subscription has to be active and current otherwise the games cannot be launched that were downloaded as free titles through the service as part of the subscription.
For a more future proof experience I'd go with the X1. If you want to scoop up a bunch of cheap games from a vast catalogue then a 360 is the better bet. The games on the 360 for Games for Gold are better too as the console has been around over 7 years and has a much more ample catalogue.
It depends exactly what you're after. If your son is looking for the latest and greatest games and sports titles are a staple part of what he plays, then consider the X1 as the games in that genre on that from this point will be truly new.
If you do decide on a 360 avoid the 4GB model. To play online (on both machines) you require Xbox Live Gold which when subscribed gives you two free games a month which have to be downloaded. Games for the 360 can be over 20GB in size these days so a 320GB or 500GB model is vital in this situation.