Boarding. My trainer assists in the care of my horse by riding him if I can't get down because of school. Plus, it's an all night watch by the owners of the property – if my horse were to colic, etc. in the middle of the night, we'd be able to catch it fast. It's just the easier, and safer option for me, though it may not be the same for others.
There's perks to both. I have my horses at home because I can always see them, and care for them! I know exactly how they're being treated and I think you bond better with your horse that way! Although boarding, you have access to indoor arenas, and rings and stuff as well as a coach on site, more horses for you baby to play with etc. Depends on your situation! If you're training a horse, boarding could be better so a coach could help you or you could do a training board! All depends on what works for you!