This entirely depends on a patient per patient level, as well as the degree of care the person needs, and the amount they are willing to pay for such care.
Generally, it is better to treat a patient in the hospital, as it is generally already equipped with the necessary equipment that is used to treat the patient's conditions. Also, if necessities exist, most departments are housed in the same building, which allows for quick treatment. In the event that it is not, the hospital has the means in transferring a person quickly to a major hospital that can provide the services.
However, there are certain instances in which caring for a patient is better at home. For example, home treatment is typical for those who are on the verge of dying, as it is nondebatable that their end is near, and instead of keeping them in the hospital, it is better to allow the family members to treat them (either per instructions, or with a home-visiting doctor or nurse practitioner), which allows for the patient to live comfortably in the place they know intimately, as well as surrounded by their loved ones.
Remember, this entirely depends on the condition of the patient, as well as the conditions of their home environment, the hospital policy, the health of the patient as well as the equipment needed to stabilize the health, and many other factors. Simply put, you cannot simply say that one is better then the other, but rather it is to be looked at in per individual case.
