For generations of New York women, one destination has loomed large when it comes to finding The Perfect Bra.

At Town Shop, the venerable Upper West Side institution, thousands of lacy, silky unmentionables are kept in boxes near a fitting area marked “Ladies Only.” Famous for saleswomen who measure with their eyes, and sometimes their hands, the store is a rite of passage for many girls on their way to womanhood, and the store, on Broadway and West 81st Street, boasts a legion of faithful customers. Before her death in 2003, the store’s beloved proprietor, Selma Koch, became something of a local celebrity after appearing on television to discuss the lost art — not science — of fitting a brassiere.

But competition is heating up for the famous store, and with the recent opening of Bra Smyth on Broadway and West 77th Street, there is a veritable bra war brewing on the Upper West Side. So far, both sides have shied away from discrediting the other. On a recent afternoon, Town Shop heir and a grandson of Mrs. Koch, Danny Koch, answered a reporter’s query about neighborhood rivalries with a coy remark. “Are there?” he said.

Leaning against a display of hosiery inside the store he inherited from his grandmother, he conceded that, “competition is going to happen.”

Six years ago, Town Shop faced a similar challenge when Victoria’s Secret opened on Broadway and West 85th Street, he said. Ultimately, more customers came to the neighborhood, but for a time Mr. Koch worried the newcomer would overshadow his store, which opened in 1936.

Of the “new kid on the block,” as he referred to Bra Smyth, he said recently, “I don’t know what they do there, but I’m not worried about it because I know what we do here.” The Town Shop stocks more than 20,000 bras for its loyal, cult-like customers.

And yet, the similarities between the stores are striking. Like Town Shop, Bra Smyth is a family business. Its owner, Diana Simon, is a third generation retailer, whose grandfather owned a department store in the Bronx. Fourteen years ago, she opened the first Bra Smyth store on Madison Avenue at 72nd Street. The Broadway store is her third, and she also owns a store in New Jersey, in addition to running a successful catalog business.

The stores themselves are both warehouse-like, filled with bras, slips, swimsuits, and hosiery. For women overwhelmed with the task of finding a bra that fits, both claim a unique ability to help.

But in contrast to Town Shop’s quaint, cramped quarters, the sleek new Bra Smyth contains racks of undergarments that customers may select themselves. At Town Shop, that task is reserved for the fitters.

A store manager at Bra Smyth, Frances Gaffney, recently said the neighborhood needed a “better” bra store. “Well, to be blunt, Victoria’s Secret doesn’t have the range of sizes that we do,” she said. She said she once got fitted at Town Shop, and although she liked the results, it can be busy on weekends.

“They did a great job, but we have different things than they do, we have more European styles,” she said. Bra Smyth also has a tailor on premises.

Among Town Shop’s loyal customer base, few believe another store can compare. Diana Berrent, 32, said she bought her first training bra there when she was 11 years old and recently returned for a nursing bra. “I’m a true devotee and I’ve referred many friends,” she said.

Not too long ago, Mrs. Berrent and a friend visited Bra Smyth and walked out with nothing. “At the end of the day, I want a bra that fits,” she said, acknowledging, however, that Bra Smyth’s new location is a “bold” move.

Maybe bra shops will cluster on the Upper West Side — a store in the neighborhood specializing in nursing supplies calls itself the Upper Breast Side — the same way that, say, lighting stores cluster along the Bowery and theaters are on Broadway near Times Square. Or maybe the Bra Smyth won’t survive in its new location anywhere near as long as the Town Shop has. One thing is sure though — in New York City, even the most established and successful businesses eventually find themselves facing competition from newcomers.