ATLANTA — Tim O’Connell’s debit card, as well as yours, is ground zero in a battle between banks and stores.

A new law that went into effect in October changed what retailers pay the biggest banks — those with more than $10 billion in assets — for processing debit cards purchases. It used to be that stores paid 1.5 percent of a sale’s total, or an average of 44 cents per sale. Now it’s a flat rate, capped at 21 cents.

Store owners who pushed for the new law said at the time the limit would save shoppers money. And that’s exactly what’s happened, those retailers contend. But banks say shoppers aren’t seeing savings. Instead, bank personnel argue, store owners are putting the savings to their bottom lines.

Meanwhile, in an attempt to recoup some of the financial losses that they say resulted from the cap, banks are eliminating debit card rewards programs and charging for checking accounts that used to be free.

So in the tug-of-war between banks and stores, do the customers win or lose? It’s a point of contention.

“It’s a complicated and somewhat murky area,” said Bob Baldwin, vice chairman of card processor Heartland Payment Systems. “It’s an ecosystem adjustment.”

Many retailers say the money they’re no longer paying to process debit card transactions is going back to customers, whether through lowered prices or new equipment to improve the shopping experience.

O’Connell, who uses his Bank of America debit card often for meals and other purchases, said he hasn’t seen a difference — not in his bank fees and not when he shops. “It’s hard to see if there are any savings as a consumer,” said O’Connell, a Gwinnett County, Ga., teacher.

Heartland’s typical customer — a Main Street restaurant — saves about $1,000 a year, Baldwin said. While their cost of business has gone down, the savings of $83 a month isn’t enough to lower prices across the board, he said. But it can mean more specials or other subtle changes.

At Atlanta’s Oxford Comics, Games & Collectibles, owner Mike Van Houten said he bought a new air-conditioning unit and new display fixtures for the store with the money he’s saved. Atlanta-based Home Depot will use its expected $35 million in annual savings, in part, to reduce prices on some items, said Dwaine Kimmet, the company’s vice president of financial services.

But other retailers say they’re using the savings to help cover rising costs.

“Is it making prices come down? No, not really,” said Kristen Smith, CFO of Abbadabba’s, an Atlanta shoe-store chain. “So many fees have gone up, I don’t foresee retail prices coming down.”