3G Capital Partners LP is known for wringing costs out of food-and-beverage businesses. Its track record for boosting sales and market share of their products is less stellar.

The Brazilian private-equity firm is currently embarked on its biggest challenge, integrating the former Kraft Foods Group into the Heinz business that 3G bought two years ago with Warren Buffett's Berkshire Hathaway Inc.

Kraft Heinz Co., formed last month, owns many of the most recognized food names in America—including eight brands with more than $1 billion in annual sales, among them Kraft, Heinz, Oscar Mayer, and Velveeta. But many of the company's brands are struggling to keep up with consumers' shift toward less-processed fare.

Some analysts think 3G could take on even more acquisitions. Activist investor William Ackman's Pershing Square Capital Management LP last week revealed that it had built a $5.5 billion, 7.5% stake in Mondelez International Inc., betting in part that it might eventually be acquired by Kraft Heinz.

A Wall Street Journal examination of the companies 3G and its founders already have invested in, which also include Burger King and Anheuser-Busch InBev NV, shows impressive increases in profit margins, but mixed performances on sales growth—other than that which comes from more acquisitions.

Since 3G bought Heinz two years ago, for example, the ketchup maker lost market share in 65% of the food categories in which it has brands, maintained share in 16%, and gained in less than 20%, according to a February report by McKinsey & Co.

Heinz has had only two major product launches in the U.S. in its two years under 3G. In February, it unveiled Sriracha-flavored ketchup, and in April it announced a consumer version of the yellow mustard it has long sold to bulk retailers and food-service customers like ballparks.

3G hasn't "done anything revolutionary or groundbreaking that worked" with Heinz products, said David Turner, food analyst at market researcher Mintel.

A spokesman for 3G Capital said the global investment firm focuses on long-term with a particular emphasis on maximizing the potential of brands and businesses. He added that the firm works in close partnership with management teams at its portfolio companies.

Kraft Heinz spokesman Michael Mullen said its strategy is "focused growth that emphasizes fewer, bigger, better innovations," and it has increased advertising media spending by 30% over the past two years, including Heinz's first Super Bowl commercial in decades in 2014.

Part of the issue is priorities, say people who follow 3G. It focuses on reducing spending through cutting staff and increasing efficiency, and only then focuses on growth, says a consultant who has worked with the firm.

3G's spending cuts generally far exceed typical belt tightening. Its use of zero-based budgeting, which requires justifying all spending from scratch annually, yields detailed savings measures, such as limits on color printing and requiring executives to share hotel rooms on business trips. The firm says such penny pinching yields savings that it invests in products and marketing.

As it scrutinizes costs, 3G also evaluates which of its brands are worth investing in. At Heinz, executives reallocated money to core products like its namesake ketchup from less promising ones, like Heinz's bottled gravy, and discontinued dozens of unsuccessful items.

While Heinz has gained market share with ketchup and its Lea & Perrins Worcestershire sauce since 2013, it lost share in areas that include Bagel Bites frozen snacks and Classico pasta sauce, according to market-research firm IRI. Its sales fell $322 million to $2.48 billion in the first quarter this year, but operating income rose 17% to $508.5 million. Kraft Heinz reports second-quarter results for its two predecessor companies on Monday.

At Kraft, 3G's approach could mean less investment in brands like Jell-O and Maxwell House as it focuses on core moneymakers like Oscar Mayer, analysts say.

3G's strategy brings potential long-term downsides. The McKinsey report, while noting that the firm has "created tremendous operational value," warns that its "focus on short-term profitability and cash flows does pose risks to brand health, particularly to future growth." McKinsey declined to comment further.

3G emphasizes its desire to grow companies, but its main means for that so far has been more deals. Burger King, which 3G bought in 2010, last year acquired Canada's Tim Hortons chain to form Restaurant Brands International Inc. AB InBev has purchased Grupo Modelo, maker of Corona beer, and craft breweries including Chicago's Goose Island.

At Burger King, sales at restaurants open at least 13 months have risen at a respectable average of 1.9% over the past three years, though that followed a rocky start with a poorly executed menu overhaul.

The company has stumbled with some products. It eliminated its chicken fries only to bring them back two years later because of popular demand. In 2013 it introduced Satisfries, lower-calorie french fries, which were discontinued within a year.

Other than that, "I haven't seen a whole lot out of Burger King in terms of food innovation since 3G came in," said a Burger King franchise operator who also owns stock in Restaurant Brands. Still, he isn't complaining: Restaurant Brands' earnings before interest, taxes, depreciation and amortization rose 14.3% to $761 million last year, excluding Tim Hortons.

Burger King and Heinz also have focused on international expansion, which Heinz has said could also benefit Kraft.

"The business is being driven by listening to consumers and delivering what they want. Innovation for the sake of innovation isn't the key driver of our business," a Restaurant Brands spokesman said.

3G doesn't own AB InBev, but its founding partners own large stakes after helping create it through a 2008 merger.

Operating income at AB InBev has grown by an average of 8.6% a year in its five years under 3G, according to A.T. Kearney. But it has lost 4.1 percentage points of its share of the U.S. beer market since its formation, according to industry tracker Beer Marketer's Insights.

AB InBev's product innovations have had limited success. It launched a margarita-flavored beer in 2012 called Bud Light Lime-a-Rita, sales of which initially surged, but recently collapsed. Chief Executive Carlos Brito said last month that revenue per barrel of beer in the second quarter was lower because of the Rita franchise's struggles. Sales of AB InBev beverage coolers, which includes the franchise, fell 23% at retail during the 12 weeks ending July 4, according to Nielsen data cited by Cowen & Co.

An AB InBev spokeswoman said it is committed to stabilizing its market share in the U.S., and that with seven of the world's top 10 beer brands, it has delivered strong commercial results in most of its top markets. She said the involvement of 3G's founding partners "drives a certain degree of best practices exchange and cultural similarities" with the private-equity firm.

Tripp Mickle contributed to this article.

Write to Annie Gasparro at annie.gasparro@wsj.com

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