Definitely at home. I've taken riding lessons at several barns and have yet to spend time at a barn that did not have major drama that resulted in my instructor leaving or the barn changing hands.  I'd prefer to be able to count on who my instructor will be and who the barn owner is.
At home, I know how the hay was selected and from where it was purchased, I know who is handling my horses, I know that they received their supplements, got their fly masks, saw the farrier, saw the vet, were regularly checked by someone who knows their behavior and can spot colic or other issues. My horses conveniently located and are kept in a location with excellent access to trails, which I don't have to share with the rest of a barn full of people. And, leaving is not a problem because I have found a professional pet sitter who I hire to watch my animals when I'm gone.