Personally, I’ve had two machines replaced by Apple under AppleCare for multiple repairs, and I opted for the advanced replacement. Once it went very smoothly, but the second time I ran into a bit of trouble. I think they give 10 days to return your machine after shipping the new machine. I sent mine 6 days after my replacement but it took a while to arrive so they charged my card for a new machine. I contacted them and they did some research and finally returned the card after about 1-2 weeks.
Business – I worked in IT for a company where I managed the acquisition and support of our Mac environment. We had a decent sized customer base (200+) and had a few machines that needed to be replaced. We always had backup machines ready for deployment, so we sent the machines before replacements. Pretty regularly I didn’t hear anything about them receiving or not receiving any communication until after we received the shipping information.
Also, if they ever offered to do it in a store, I chose that option. Much better to just drop it off and leave with a new car the same day.