I prefer an agency where the care givers are employees of the agency and not merely "referred" to the customer. With a referral service all of the liability falls on the person requesting the service not to the agency. But I have yet to find a service that doesn't list themselves as a "referral." Are they all set up this way?
I used a company called Home Instead and all their caregivers are employees of the company. I was quite pleased with the Agency. The Agency was licensed, bonded, insured, and had workman's comp for their employees. You pay the Agency and the Agency pays the caregivers.
The Agency sent out a Rep to check over the house and to meet my Dad, thus the Rep interviewed me, Dad, and I interviewed her, she asked the right question. Dad had a variety of caregivers who come in to help him and from that group he told me which one he enjoyed having around the house, who had his same crazy sense of humor, and he felt comfortable talking. It is so important to find a Caregiver, as Gladimhere above had mentioned, that is a good match :)