For McDonald's (MCD), the biggest worry of the moment may be Doctor's Associates Inc.

No, that's not a medical organization. It's a business that owns a very large restaurant chain. While it's true you could be excused for not knowing them, you're almost certainly familiar with their well-known operating unit. That would be Subway, the Milford, Conn.-based submarine sandwich shop that's grown at an extraordinary rate and is approaching 40,000 restaurants worldwide. It's nearly doubled its store count since 2003, the year it reached 20,000 units.

Shouldn't the headaches for Ronald McDonald & Co. come mainly from Burger King (BKW) and Wendy's (WEN)? They without question pose their own challenges, but, according to a report this week in Advertising Age, Subway also appears to be prominent among the things that cause angst for the Oak Brook, Ill., burger giant, in particular with regard to its appeal to the millennial generation.

Citing an internal company memorandum it obtained, Ad Age says McDonald's has referred to the wide launch of the chicken McWrap as the "Subway buster," viewing it as a product that will help keep younger eaters from choosing the sub chain when they're looking for a fast meal. McDonald's has learned that, without the McWrap, some 22% of diners in the roughly 18-32 age range would pick Subway, the article indicates. In addition, the quarter-pounder seller says in the memo that it "is currently not in the top 10" of the demographic's favorite chow establishments.

Lynne Collier, a Dallas-based restaurant analyst with Sterne Agee, has followed McDonald's for around three years, and she found it a bit curious that Subway would be at the front of the company's mind. After all, in addition to the found-everywhere chains noted above, other similar-to-McDonald's and quite widespread restaurants include Jack in the Box (JACK) and Sonic (SONC).

"I don't automatically think Subway," she says. "But apparently they are viewing Subway as somewhat of a major competitor."

What the (young) people want

Stresses about the eating trends of those born in the 1980s and forward aren't new, says Nick Setyan, a restaurant analyst with Wedbush Securities in Los Angeles. "The problem with millennials, that's been a category-wide problem," he says. "It hasn't just been a McDonald's problem."

A crucial influence in that has been the advent of "fast casual" chains, names like Panera Bread (PNRA) and Chipotle (CMG). Companies in this group might, for instance, go out of their way to emphasize ingredient quality or awareness of social issues, he says. That's important to the young, and it's fine that, on the price spectrum, these restaurants would be located a step above a McDonald's or a Burger King for most menu items.

Source: Subway data from Entrepreneur. McDonald's data from SEC filings.

Fair or not, Subway has gotten to be known for Jared Fogle, the long-time spokesman whose story centers on his shedding 245 lbs., aided by a diet that depended significantly on the company's sandwiches. Also fair or not, McDonald's came to be associated with "Super Size Me," the Morgan Spurlock movie in which the filmmaker gained a good bit of weight after eating only McDonald's food for a month. [Editor's note: Spurlock has a video-production relationship with Yahoo.] Of course, it has bulked up its healthier menu items, such as salads, and moved to address worries about trans fats in recent years.

Still, millennial eaters are discriminating, Setyan explains, and they feel perhaps more strongly than prior generations about the make-up of their foods. "It really is about transparency. That's the heart of it," he says. Setyan doesn't officially cover McDonald's, but his universe does involve analysis of a number of restaurant chains, including hamburger sellers.

He says negative stories such as the "pink slime" uproar last year tend to hurt fast food restaurants -- what are in the industry called quick-service restaurants, or QSRs -- causing the press and consumers to fret about quality.

"On the other hand, you have the quick casual guys like Chipotle that have made part of their branding strategy the fact that they are so transparent," he says.

Collier agrees that many of today's younger food buyers aren't just picking up a meal without considering what they're putting in their mouths.

"That younger audience is definitely very important for all QSR restaurants, including McDonald's," she says. "I think that age group is focusing a little bit more on quality, healthy foods." Citing her own children, who would qualify as millennials, she says, "they're a lot more sophisticated about food and quality."

An important audience

Regardless, McDonald's, on which Collier has a buy rating and a $101 stock price target, is a "dominant force" in the sector. "They're far ahead of many of their other competitors in terms of product development, in terms of marketing power, in terms of management expertise," she says.

In response to a request to discuss the memo, McDonald's said in an email that "we don't comment on leaked information." However, the company did add that "[m]illennials continue to be an important audience for us, as are all our customers." The statement also said the McWrap "has been well-received by customers of all ages" and is another menu option for visitors who want variety.

As to where it places among restaurants favored by the millennials, it isn't clear without the memo which survey McDonald's is relying on to make that determination. However, food industry data collector Technomic issued a press release in May 2012 that dealt with the eateries favored by youth.

Looking at three attributes this segment views as "highly valued" -- social responsibility, food quality and support for local community activities -- McDonald's wasn't among the top-ranked. That said, the publicly available part of the study highlights only a trio of 50 total areas that were evaluated in the research. It does note that chains including In-N-Out Burger, Cracker Barrel, Chik-fil-A and Red Lobster scored high marks.

Source: Technomic. Restaurants highlighted in green appeared twice in the rankings.

Though 10 discrete restaurants were named in the release, again, it isn't a foregone conclusion this is the list to which the McDonald's memo was referring. A Technomic representative said the firm couldn't comment on an internal memo belonging to a client.

Subway didn't respond to an emailed request seeking a quote for this article.

Beyond Subway, Setyan notes that, even within the hamburger sector, the "better burger" category, with names like Five Guys or Smashburger, has been surging and presenting another enemy for McDonald's. They appeal more to millennials with higher-end products and compete with pricier McDonald's fare such as the Angus burgers -- items that reportedly may be on their way toward disappearing from the menu.

"A millennial will choose to go to one of those brands as opposed to McDonald's," Setyan says. "It's really been a, I would say, structural issue over the last 10 years, not something that's come up recently."

You tell us: Is McDonald's right to be worried about Subway? Should it be more concerned with "better burger" options?