Nate Oman has an interesting post about how, for a slave in the American South, it may well have been worse to be owned by a church than by a private owner. Nate writes (based on an account of a friend's doctoral research) (paragraph break added):

In most congregations, church property was not controlled by the minister but by the vestry, a committee of powerful members of the congregation. The minister was often simply a salaried employee who served at the pleasure of the vestry. The vestry, in turn, tended to be cheap. They weren't always excited about expending scarce church funds of things like doctors for injured slaves or other expenditures to ameliorate their condition. In particular, when a church owned slaves but lacked the capital to provide for them, it was sometimes extremely difficult for the vestry's to raise funds for slave-related expenses.

In contrast, slaves that were privately owned were regarded as an expensive investment that many owners were unwilling to wantonly harm through a false economy. In short, institutionally owned slaves where quite literally victims of the tragedy of the commons.

I recall reading something similar in George Reisman's The Government Versus the Economy (note: this is not an endorsement of that book generally), about, if I remember correctly, conditions for the slave in private slavery versus "state slavery," in the form of totalitarian labor camps.