You didn't mention what kind of budget this guy has. Frankly, I'd buy both. Trying to make a gun do too much is not a good thing. AR-15s don't make good CQB weapons because of their nasty tendency to overpenetrate with anything but a frangible round. A shotgun mounting a pistol grip (preferrably the horizontal type that looks like a cut-off buttstock) is also much easier to handle indoors than an AR. And how often has anybody needed to take a 200 yard shot in a home defense situation?
I would say a shotgun is superior, in 20 guage. Everyone in the family can use it and a 20 guage pump is a lot cheaper than the cheapest AR. A couple of loads of buckshot will put a bad guy down, and the pellets are unlikely to go through his body.
Buy one for plinking and one for home defense, don't short change your personal defense for a "fun gun"