My experiences with both First American and American Home Shield were very positive, save for one incident. The repair person claimed that my dryer was working when, in fact, it wasn't then switched his story to say the repair was not covered. I called AHS, explained what happened, and they sent a different technician. As soon as he opened the door and smelled the residual burnt metal smell from when the capacitor went out he knew what the problem was. He ordered the part, it arrived in a few days, and he returned to fix the problem. Note that I only paid one deductible.
I think the experiences vary by region. In San Diego, most of the repair people were independent contractors. One of the guys (plumber sent to fix my dishwasher) became my plumber.