Think about all the sandwich shops in your neighborhood. These might include Subway, Quiznos, Panera Bread (PNRA), Firehouse Subs, and more. While Potbelly Corporation (PBPB 1.88%) – owner of Potbelly Sandwich Works sandwich shops – might be growing, the more it grows, the more competition it's going to run into. This doesn't include other eateries such as McDonald's, Burger King, Wendy's, and many more. The question is whether or not Potbelly can grow despite all the competition and it has important implications for Foolish investors.

Reasons for optimism
The first point is perhaps the most often overlooked, which is that Starbucks CEO Howard Schultz was an early investor in Potbelly. Howard Schultz is easily one of the smartest and most strategic CEOs in the world. Therefore, this is a positive sign.

Potbelly CEO Aylwin Lewis also has 28 years in the restaurant industry, primarily thanks to service as the President, Chief Multi-Branding and Operating Officer of Yum! Brands. He was also CEO of Kmart when it merged with Sears, and he's on the Board of Directors for Disney and Starwood Hotels & Resorts Worldwide.

Lewis was recently interviewed on NASDAQ CEO Signature Series. In this interview, Lewis stated that the goal is to grow Potbelly into a global iconic brand. Currently, there are approximately 280 company-owned and six franchisee locations in the United States, and 12 franchised locations in the Middle East.

The Middle East might seem like a strange choice for a sandwich shop like Potbelly, but one of the largest Starbucks franchisees asked to bring Potbelly to the Middle East, and Potbelly agreed. Potbelly aims to have mostly franchisee locations overseas while keeping the majority of domestic locations company-owned.

On that same interview, Lewis promised double-digit growth for the foreseeable future. Potbelly aims for 300+ stores by the end of the year, and ultimately wants to be in as many neighborhoods as possible.

When asked about a sandwich shop's sensitivity to a weak economy, Lewis stated that the company's customers are loyal, and that they enjoy the high-quality food, musicians, warm atmosphere, and friendly service. In his opinion, it's a slice of heaven, and you will always leave with a smile -- whether real or symbolic.

The young and the restless: Potbelly vs. Noodles & Company
Both companies went public this year. For Potbelly's IPO, shares were expected to be priced between $12 and $13. They were priced at $14, and the stock ran to a peak of $33.78 on the first day of trading.

Noodles & Company's (NDLS -5.60%) IPO was similar. Shares were expected to be priced at $15-$17, but they were priced higher at $18. The stock ran to a peak of $47.60 on the first day of trading.

These massive one-day moves are very 1999-ish, and they have led to extreme valuations. For instance, Potbelly is currently trading at 74 times forward earnings, and Noodles & Company is trading at an even loftier 87 times forward earnings. Therefore, almost all potential good news is priced into both companies. While upside potential still exists, the downside risk is much higher. Any surprising bad news could lead to a gap down.

Foolish investing is about selecting steady long-term winners that have proven underlying business models. Dividends don't hurt, either. While these two companies are young and offer a lot of growth potential, they're not proven yet, the valuations are too high, there are no dividends, and no investor is interested in risking a lot to profit a little.

If you're determined to choose between one of these two companies, then it should be noted that Potbelly sports a profit margin of 8.20%, considerably higher than Noodles & Company at 0.82%.

Panera Bread by default
I recently wrote an article titled, "Is It Time to Give Up On Panera Bread?" Panera Bread is a quality and highly profitable company. The problem is that it doesn't offer consumers a unique experience anymore. Many other restaurants witnessed Panera Bread and Starbucks succeed with their comfortable atmospheres and free WiFi, and they have copied that approach. Panera Bread is still delivering solid numbers, but management has recently reduced guidance. Put simply, Panera Bread is maturing. It's highly likely to remain a quality company, but its growth seems to be slowing.

All that said, Panera Bread is trading at 23 times forward earnings while sporting a profit margin of 8.43%. Therefore, if you're just looking at simple numbers, it's easy to conclude that Panera Bread is likely to offer a lot more investor safety than Potbelly or Noodles & Company.

The bottom line
Potbelly is a growing company run by experienced management. On the other hand, no one knows how the company will fare when it pits itself up against a multitude of competitors in various restaurant segments. Be sure to watch comps numbers for an early indication of how the company will perform in the future. In the meantime, Potbelly's valuation leads to downside risk outweighing potential rewards. Foolish investors should weigh the facts carefully before making any investment decisions.