A recent study showed that since family caregivers often have more than one role to perform (caregiver, mother, father, employee), self -dissatisfaction is experienced as it is impossible to fulfill all the roles all the time. Do most caregivers find this true?
Reference
Dhar, R. (2012). Caregiving for Elderly Parents. Home Health Care Management & Practice, 24(5), 242-254.
But the fact that self-dissatisfaction is inevitable does not really address the question of your title. Keeping the family member at home or the home of a relative may still be the best of the imperfect choices available.
The "best" solution is for no one to develop chronic conditions that require a lot of care. When that happens then we can discuss the best environment. Until then we can only strive for what seems to make sense for this family in their particular circumstances.
Your question is a broad one. The answer differs widely, depending on the personalities of the care receiver and the caregiver, as well as their financial resources. With life being so long now, I believe that the best answer for all involved is for the elder person to live around people their own age. An elder may want to remain at home or with family, but they tend to isolate. If they can afford it and their health is good enough, living in an independent or assisted living community would probably be a lot more stimulating mentally and physically. We family caregivers may actually be doing a disservice in enabling a behavior that makes life miserable for both the care receiver and caregiver. It's better to be out among people than sitting home alone, watching TV. That is no way to live.
If there was any One thing that we would have done differently, it would be to inforce that my husband's Dad live independently from us, and to have found him the nessesary aid and care to support this. I would definitely agree, that having my FIL living with us has made me/us, miserable at times. It is impossible to please everyone concerned, all of the time, which means that you as the caregiver, forgo's enjoyable activities most of the time. No, it's not fair, nut this is the hand that we have been dealt, and it is a constant learning process, and it SUCKS!