Late to the party but I was out of town for a week. I've had AHS for a few years. Let me sum up the good and bad:

BAD
Slow to respond. If your A/C goes out, you're probably not going to have someone show up that afternoon. Then again, in order to get that kind of service, you're going to be paying out of the nose.
Don't expect to get new stuff, especially if it's A/C related. I haven't had any calls about appliance-related issues yet. Expect them to limp along your equipment as much as possible; they will exhaust all other options before they even think about a replacement.
Contractors generally have poor reviews on Yelp.
Read the fine print. When it comes to A/C repairs for example, they usually exclude the cost of refrigerant to a large degree.

GOOD
It does save a lot of money if you have major repairs.

My experience with their contractors has actually been pretty decent. They generally get crappy reviews on Yelp, but that's because they're through AHS and people are mad at AHS as much as anything else. So far, I've had two major A/C issues and they were both fixed to my satisfaction. I had a call at my daughter's condo, and that was handled well also. Got one this coming week for a plumbing issue at the same condo and I'd rather pay the $75 than drive an hour each way and hunt down repair parts.

Personally, I think it's worth it IF you have some expensive equipment that's nearing end-of-life (Multiple A/C units in my case) or a property that has tenants where it's not convenient to get to. Yesterday, my daughter's roommate sent me a text that the faucet is leaking from around the faucet body. No damage under the sink and no wet spots there; that's something I'd rather pay for someone to go out and fix instead of taking half a day or more off of work.