There's a new salvo in the competition at the biggest big-box stores — and it may pay off for consumers this weekend.

Costco Wholesale Corp. and its new credit card partner, Citibank Visa, stumbled in the transition scheduled last week away from the retailer's longtime reliance on American Express. And Costco's biggest rival, the Sam's Club unit of Wal-Mart Stores Inc., is scrambling to capitalize.

Many Costco customers never received the Citi card that was supposed to succeed their American Express card. Others had trouble activating the new card. Citigroup logged more than 1.5 million customer service calls, according to Citi spokeswoman Jennifer Bombardier. Many customers were unable to get through or put on hold for up to an hour listening to apologies for "unexpectedly high call volumes."

"Citi completed one of the single largest portfolio conversions in history," Bombardier said. "We sincerely apologize to those who have been inconvenienced."

Sam's Club's response? It will allow people who don't have a Sam's Club membership but do have a Costco membership card to shop its stores through July 4.

Costco members who don't have their new Citi cards can bring in an old card or their inactive American Express card. Purchases can be made on any Visa, MasterCard, Discover or American Express cards.

Customers walk toward a Costco Wholesale store in Nashville, Tennessee, in 2015. (MUST CREDIT: Bloomberg photo by Luke Sharrett) ORG XMIT: 581699321

In an effort to distinguish itself from Costco, Sam's now offers in-store pickup for online orders and self checkouts. But it has lagged behind Costco for nearly a decade. Since 2007, Sam's Club has only once reported higher annual same-store sales growth than Costco.

Sam's racked up sales of $58 billion last year from its 47 million members in more than 650 stores. Costco tallied $114 billion in sales from 81 million members in nearly 700 stores.

Sam's Club CEO Rosalind Brewer said recently that Sam's has started to cater to higher-income customers. "This is absolutely a reset for our business," she said. "We realized that we have the ability to take Sam's to a higher household income."

Some Costco members flying over to the Sam's Club side have experienced a little turbulence. The Consumerist reported earlier this week that not all Sam's Club employees were aware of the temporary offer. Some Costco members were turned away and others had a 10 percent nonmember surcharge tacked on. No surcharges are supposed to apply through July 4 for Costco members at Sam's Club.

The advantage of both warehouse clubs is that customers can cancel at any time and receive a membership refund. In another sign that Sam's Club wants to take advantage of Costco's stumble, the Living Social daily deal site is currently offering a one-year membership to Sam's for $25, a $20 savings. The deal also includes a $10 e-gift card and $100 in discounts on select items.

People considering a membership in either club can go online to compare the two. Costco usually edges out Sam's Club despite Costco's slightly higher annual fee. A comparison by Cheapism.com gave Costco better marks for its pharmacy, premium membership cash-back program, customer service and store brand quality. Sam's received better marks for its lower annual fee and multiple payment methods. Prices at the two competitors varied but were about the same on average.

Sam's Club has locations in Apple Valley, Bloomington, Eagan, Fridley, Maple Grove, St. Louis Park, Shakopee, White Bear Lake and Woodbury. Costco is located in Coon Rapids, Burnsville, Eden Prairie, Maple Grove, Maplewood, and St. Louis Park.