Walmart's relentless price war is crushing America's biggest grocer

Walmart and Kroger are in a price war, and Walmart is winning.

The retailer's groceries are about 4% cheaper than Kroger's, according to a recent price check by Barclays.

Analysts compared prices on a basket of 78 identical items at Walmart and Kroger stores in Nashville to determine which retailer was cheaper.

Walmart offered lower prices than Kroger on 74% of the items checked.

Barclays found the biggest price differences between the two retailers on non-perishable and frozen items, where Walmart had a 5.6% price advantage over Kroger.

Kroger was cheaper than Walmart in the "fresh" category, however, which includes proteins, dairy, and vegetables.

Kroger was 3.3% cheaper in that category, but mostly due to steep discounts on a small number of items including eggs, apples, green grapes, baby carrots, bell peppers, and chicken breasts. Excluding those items, Kroger's "fresh" products were 15% more expensive than Walmart's, according to Barclays.

Both Walmart and Kroger have been aggressively lowering prices to better compete in the increasingly crowded grocery market.

But Kroger appears to be losing the battle.

The chain's same-store sales, or sales at stores open at least a year, fell 0.7% in the most recent quarter, marking the end to a staggering 13-year streak of quarterly same-store sales increases.

The company blamed food price deflation for the decline, but its clear that Kroger is also feeling pressure from competitors.

Barclays analysts said Kroger may have a hard time catching up to Walmart on price.

"While we feel Kroger has clearly proven over the years that it is a superior operator, the magnitude of Walmart's investments may prove difficult to overcome," analysts wrote.