Whole Foods is battling Walmart for budget shoppers following its acquisition by Amazon - here's where you can get the better deal

Whole Foods is slashing prices following its $13.7 billion acquisition by e-commerce giant Amazon.

But can the grocery store ditch its "whole paycheck" reputation to compete with Walmart, the reigning king of American budget shopping?

In an effort to see how Whole Foods actually measures up against Walmart when it comes to grocery prices, we compared the prices of 31 items sold at a Whole Foods store in Durham, North Carolina, with a nearly identical set of items at a nearby Walmart.

The Whole Foods basket was $30.02 more expensive than a basket of the same items purchased at Walmart.

The bills came to $137.89 at Whole Foods and $107.87 at Walmart, after we accounted for the products' varying package sizes and calculated those differences into the final price. In other words, shopping at Whole Foods is almost 30% more expensive than at Walmart.

A $30.02 difference is a significant gap - but a closer look at the numbers reveals some reasons to believe that Whole Foods and Amazon still have a shot at winning over bargain shoppers.

Walmart's prices were less than Whole Foods' on almost every item.

However, there were a few areas where Whole Foods triumphed: bananas, peanut butter, and organic butter. Some other organic grocery staples, such as grapes, watermelon, and eggs, came within a few cents of Walmart's price.

Many of these items had their prices slashed in late August, on the day the Amazon acquisition formally went through. Organic bananas, for example, went from 99 cents a pound to to 69 cents a pound, matching Walmart's price exactly.

These price cuts have played a crucial role in allowing Whole Foods to come close to competing with Walmart's prices.

While Whole Foods has been trying to win over value-oriented shoppers for more than two years, it took Amazon's acquisition for the retailer to actually slash prices to figures near Walmart's. The fact that Amazon has promised "more to come" bodes well for the retailer's ability to lower prices in the future.

In a few cases, Walmart's prices are lower because Whole Foods simply doesn't sell non-organic, or "conventional," versions of certain items, including coconut oil and quick oats.

However, Walmart's prices are significantly lower than Whole Foods when it comes to selling the same name-brand items. Justin's Almond Butter is more than $2 less expensive at Walmart, and Annie's Mac and Cheese is almost half the price.

Whole Foods has historically stocked a plethora of more expensive gourmet, organic, and all-natural brands, like Cypress Grove cheese priced at $32.99 a pound and $8 Fine & Raw chocolate bars. The grocery chain refuses to sell many of the popular brands, from Oreos to Doritos, that fill Walmart's shelves.

Even when there is overlap and both retailers sell the exact same brand, Walmart has the lower price.

Whole Foods' post-Amazon acquisition price cuts have had a major impact, especially on produce and some of the retailer's 365 brand items.

However, if your top priority is low prices, Walmart still reigns supreme - by a pretty significant margin.

Here's the full list of our results:

*The Durham Whole Foods only sold organic coconut oil and quick oats, while the Walmart did not sell organic brown sugar. Business Insider compared the lowest-priced options available.