I was always under the impression their differentiator is speed, convenience, and selection. They're marketing is heavily towards how quickly and how conveniently they can get anything you want to you.
Either way, that's exactly my point. Why would you compete with Amazon on price? They can get anything in larger bulk quantities than you ever could.
I do a substantial amount of personal shopping on Amazon -- 6-7 orders a month -- and they are rarely the cheapest option. Shipping & hassle-free returns is the value-add.