To evaluate Walmart’s retail market performance in comparison to the other major chains listed in the question—Target, Costco, and BJ’s—one will have to do some research and figure out ways to measure their success.
One way to assess their performance is by identifying the revenues of the four companies. According to their 2019 annual report, Walmart made $514 billion in revenue. Target’s revenue was far less. According to their 2019 annual report, they brought in around $78.1 billion. Costco’s reported revenue was less than Target. In 2019, their revenue totaled $3.6 billion. BJ’s annual revenue was higher than Costco’s, but less than Walmart’s and Target’s. BJ's supposedly brought in around $13 billion in 2019.
If one bases their comparison on revenue, it’s safe to say that Walmart has outperformed the other three businesses. Yet revenue doesn't tell the whole story. Other areas to look at that should help paint a more complete picture could connect to the online strategies of Walmart and the three other stores.
In 2019, Walmart redesigned their website. Compare Walmart’s digital presence—a key element in retail—to that of Target, BJ’s, and Costco. Parse their websites and their apps. Try to get a gauge on how popular they are amongst consumers. A store’s online and digital presence tends to reveal a lot about how well they are performing.