As I'm standing in a Home Depot store struggling to find an item, I can pull up the site, verify they have something in stock, and get a map of the store showing me where that thing is. This is an incredible consumer experience. Even when the thing I want isn't where it's supposed to be, showing that to a staffer usually gets an "Oh, yeah, we moved those to aisle Foo last week" response.
On the flipside, when I go to WalMart's site the default search behavior is showing me numerous items from 3rd-party sellers that are not and will never be available in-store. They do have inventory information but you have to specifically filter for it and I find it much less reliable and difficult to navigate than Home Depot's.
Hopefully they take pages from each others' playbooks.