I honestly think there are a lot of benefits either way. At a boarding place there is almost always someone on site, and when you go on vacation, you don't have to worry about paying someone to come out and feed. A lot of barns around here do clinics, they have the vet come out and do all the horses at once which cuts down on costs for the individual boarder, same with the farrier. There are people you can hook up with and go riding, talk to, hang out with ect. On the flip side though, having them at the house you can be so much more particular about what they are fed, exactly how much, how their stalls and/or pastures are cleaned. They are just a short walk away, if something goes wrong, you can generally catch it early, and you don't have to drive 10 or 15 miles down the road just to get to the horse. And the biggest one for me, is that you get to know your horse so much more intimately than you would with them at a boarding facility.
If I had the money, and the stability, I personally would move to have them at my house. I would probably board for a bit as I looked around, partially so that I could meet the horse people in the area, but ultimately I'd want them at home. For me, I would feel better knowing that I know my horses extremely well, and if something happened like colic, I would be able to tell so much sooner that the horse was even a tiny bit off, than the BO at a boarding facility would, and just those few minutes can sometimes mean the difference between being able to treat the problem, and having to put the horse down. Hopefully you can find the perfect place with an awesome landlord if this one doesn't change his mind.