It's really going to depend on their exact level of independence.
It could happen that they need full time professional help, and professional help is dedinately not minimum wage. If they come from an agency, it's almost a certain bet it is going to cost more at home. Remember that liability and worker's comp insurance will be your responsibility, as will the various payroll tax deductions and filings. A top level facility is going to have 5 residents per staffer. The average is around 10:1. At home care is going to be 1:1, twenty four hours a day. Most of us couldn't bear the costs.
It's also true that most seniors are going to be happiest at home, with their own furniture, room, and perhaps pets. You will have to run your own numbers to see how it compares. Keep in mind that this might be best for the senior, but not everyone could stand the stress.