@cg006 Are you sure that Amex will start their extended warranty after Applecare+? I don't think that's was how they did a few years ago, but things change.
To the OP, it really depends on your credit card. The one I use now Citibank Costco adds 2 years to the manufacturer's warranty. If you purchase an extended warranty, the Costco warranty starts after the extended warranty expires. So in my case, I'm covered for 3 years on Apple product without any extra cash outlay. If I add Applecare+, I'm covered for 4 years.
The caveat being that I'm only covered up to the amount that I charged on the card. If I paid for half of it with a gift card, then Costco will only cover up to half the price. That's why I won't go on an NEXT type plan, because I won't have any extra coverage on an iPhone bought that way.