Amazon's catalog is so much bigger than Costco's along two axes; more kinds of products, and more varieties of a given kind of product. The latter axis can be good for Amazon, since people have different utility functions, brand loyalties, etc. But one thing I like about Costco is that their catalog seems to be curated; whatever brand/model of a given thing they happen to carry, it's usually pretty decent. Amazon, by comparison, carries good and crap versions of pretty much everything, but you can use the customer reviews to separate the wheat from the chaff). By removing the paradox of choice, Costco not only reaps the usual benefit on the buyer's psychology, but is also able to negotiate better wholesale prices on the items they buy due to higher volume. Maybe that's a way for them to compete?
As for "offer something better other than price", most people point to customer service, and in my experience Costco's customer service completely blows away Amazon.
They might compete of some selected products, but it's a long way to the "we have it all" of Amazon.