Over the past few years, traditional supermarkets have focused more on the "perimeter" -- fresh foods, prepared foods, organic foods, etc. They ceded the "center store" (dry goods, paper goods, cleaning supplies, etc) to Walmart, Target, Costco, etc.
Many of the supermarket chains made the worst business mistake of all -- they forgot about their core business when chasing new money.
When it comes to supermarket fare, Walmart has two types of stores. The one that offers the larger supermarket food selection is called a superstore.
The normal Walmart offers food items, but in a much more limited format. The superstores carry a wider variety of goods, especially in the more traditional supermarket fare of meat, fish, produce and other staples.
Walmart generally tends to offer lower prices than supermarkets on many of the non-perishables including salad dressings, bottled sauces, condiments, baking goods, and some frozen food items. Milk and soda also come in at lower price points than traditional supermarkets.
However, that said, there are a number of areas where a well managed supermarket can shine.
While the Walmart superstore has a much wider variety of items than their traditional stores, the availability of many items reflects their penchant for purchasing manufacturers' overstock. So, it is entirely possible to pick up an item at a great price one week only to not find it on subsequent trips.
Supermarkets tend to have a greater consistency when it comes to their merchandise offerings.
Although Walmart superstores have meat and produce areas unlike their normal stores, they seem to lack the manpower to maintain them to the same degree as your average supermarket. Produce especially, requires constant pruning to remove decaying items to maintain appeal and the appearance of freshness.
Supermarkets tend to do a better job at produce management.
Also, Walmart tends to merchandise produce like it merchandises boxes of cereal on sale, often in non-refrigerated stands with items piled on top of one another seemingly with greater deference to limited shelf space than item presentation.
Most supermarkets appear more than capable of competing with Walmart on meat and fish prices. Supermarkets tend to have weekly offerings in these categories as loss leaders to entice store traffic.
Walmart seems to rely on its reputation for generalized lower pricing to hope shoppers will purchase lightly discounted meat products simply out of convenience since they are already in the store.
Supermarkets tend to fare better in urban settings where Walmart competition is nil.
Also, depending on a supermarket's location relative to a working class demographic, some individual supermarkets are devoting more space to in house, higher margin prepared foods that carry an appeal to working adults less inclined to start meal preparation upon returning home from a full day's work. Prepared dishes and buffet type food presentation afford attractive variety, convenience, and nutrition exceeding fast food fare.
The bottom line is that supermarkets are probably losing market share in the staple and non-perishable item areas, but less so in the produce and meat areas where freshness and product maintenance are key factors.
Those supermarkets who can adapt to their demographic customer needs are better positioned to maintain and grow market share despite Walmart's presence.