Not in the areas of California I frequent. Walmart is usually the cheapest around here; heck, even Target beats Safeway on some items. On the other hand, Walmart is also usually the worst at stock rotation.

>Walmart isn't a budget grocery store,

The answer to this is complex, it has any number of products that are cheaper than products of similar quality from any other store. Places like Safeway/Aldi typically beat on price on very generic items that may or may not have similar quality.

The biggest thing to watch for at Walmart is price discrimination dependent on location. Back in the days I used to shop with them (read made less money) picking a store in a poorer neighborhood could save $10 to $30 dollars on the same car of items.