This may not be an either-or situation. When my mother needed 24-hour care, we used 2 agencies and some private caregivers as well. This was NOT in a small town, either! To be sure you always have coverage, you probably should also be using more than one agency.
I worked for Home Instead years ago. They didn't even require me to have experience caring for elders, just that I show up and do whatever was asked of me. Cleaning, cooking, shopping, driving an elder to a hair appointment, etc. They did check my character references, but not even my driving record! I had been a stay at home mom for quite awhile so i had most of the skills necessary, but no experience showering an elder or dealing with dementia for instance.
We don't really know your Dad, nor either of the agencies, and haven't done any interviewing nor know the needs, so this has to be entirely up to you. Make a list of pros and cons you are aware of, chose the agency best for you, and know the other is there is the first doesn't work out. Always good to have choices tho sometimes it just adds to the trauma of decision making. I wish you good luck and hope you will update us on your experience.
Have you considered Care.com?