Accidental damage coverage wasn't added to AppleCare until the switch to the Plus plans, with a corresponding price increase.
AC+ is really a combination of a warranty and support extension with accident insurance, and optional theft/loss coverage at additional cost.
With a good card program, it doesn't have to be a choice between one or the other; it can be beneficial to have both. Again, using AMEX as an example, one can still purchase AppleCare, and AMEX's extended warranty kicks in
after AC expires, so for a Mac, there is
four full years of coverage. That fourth year of coverage may not cover accidents, but it's
free, and well into the product's lifetime.
Some time has passed since that story was written, but I haven't noted any change in terms to AMEX's program. In fact, they enhanced it last year as others are cutting back.
Citi's Costco Visa is the only card that doesn't seem to be cutting benefits.
It should also be noted that many of these benefits are secondary, especially the rental car coverage, which covers what one's primary car insurance does not cover. AMEX offers primary rental coverage for a small fee, but one has to enroll in the program, after which it will automatically add the coverage to each rental made with their card.
Not trying to sound like an AMEX cheerleader, but it's an easy choice when I make big purchases. If my Citi card didn't have such a long history (it was at one time the original Apple credit card), I'd have closed it, based just on their customer service. Some don't call it Shitibank for nuthin'.
No matter, the bottom line is one has to read the fine print, for any card.