As the coffee war continues between QSRs, coffee franchises and c-stores may be feeling the pinch more than the local Dunkin’ Donuts, Reuters reported.

Although McDonald’s has tried to undercut competitors on price, Dunkin’s market share in coffee is steady and growing, Mark Nunnelly, managing director at Bain Capital, said at the Reuters Private Equity and Hedge Funds Summit in New York.

“The big hurt has not been Dunkin to McDonald’s or McDonald’s to Dunkin,” Nunnelly was quoted as saying. Instead, he said local convenience stores are being hurt by competition from Dunkin’ and McDonald’s.

Nunnelly, whose firm is one of three private equity owners of the doughnut chain, said Starbucks Corp has been hurt the most by the price war and the weak economy.

“The higher-priced players at $4 or $5 for a latte have obviously had the toughest year through the crisis,” he said. “The more accessible price point players like Dunkin’ and McDonald’s have fared better through that period.”

More consumers are trading down from expensive drinks to cheaper plain coffee rather than switching among the various outlets, he told Reuters. “If you look at Dunkin’s comps in coffee and McDonald’s comps in coffee, I think you would say you’ve got a pretty loyal set of customers both places, that the price points aren’t different enough,” he said.

McDonald’s has said strong sales of its McCafe line of coffee drinks were in part responsible for a surprise 1% increase in same-store sales in December, but January U.S. same-store sales declined 0.7%, according to Reuters.