BERLIN—For decades, Siemens AG lived in the shadow of General Electric Co., with the German engineering and technology company often mimicking its competitor’s practices and managers looking to it as a benchmark.

Now, it’s GE that is catching up with its rival’s moves.

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BERLIN—For decades, Siemens AG lived in the shadow of General Electric Co. , with the German engineering and technology company often mimicking its competitor’s practices and managers looking to it as a benchmark.

Now, it’s GE that is catching up with its rival’s moves.

GE’s announcement this week that it will split into three public companies follows Siemens’s strategy of spinning off some of its major divisions in recent years. Under pressure from investors, the German company shifted from a conglomerate into a company focused on faster-growing and higher-margin software and technology, shedding its healthcare and energy businesses.

This change of strategy helped Siemens overtake its U.S. rival in market capitalization after being as much as four times smaller in the mid-2000s.

“Simply, GE is just late to the de-conglomerisation party,” investment bank Jefferies wrote in a report to clients this week.

Siemens Chief Financial Officer Ralf Thomas said the company couldn’t help feeling vindicated after the GE announcement.

“They have to act,” Mr. Thomas said Thursday. “We had the opportunity to act from a position of strength back then when we were shaping our plan.”

GE Chief Executive Officer Larry Culp said in an investor call this week that the “momentum we have built puts us in a position of strength” to divide into three businesses that can realize their full potential.

On Thursday, Siemens reported better-than-expected sales and orders during the quarter despite continuing supply chain disruptions, and the company also said it would increase its dividend.

Siemens, whose activities now center on industrial software, automation and mobility, said sales rose 18% to 17.44 billion euros, equivalent to $19.98 billion, in the three months to the end of September. Company shares closed up around 3% in Germany.

Continuing its spinoff drive, Siemens confirmed Thursday that it would carve out its large-drives unit, which makes heavy-duty drive systems for ships, mines and mills, into separate legal entities.

A Siemens Gamesa factory in Hull, England, produces blades for offshore wind projects.

Photo: paul ellis/Agence France-Presse/Getty Images

GE’s moves raise pressure on Siemens to further trim its stakes in its recent spinoffs to streamline the company even more, investors and analysts say. Some say Siemens hasn’t gone far enough and still retains a great deal of complexity, with some calling for it to spin off its mobility division.

Siemens has a 75% stake in Siemens Healthineers AG , which works in the field of medical technology, and 35% in

Siemens Energy AG , which makes gas turbines and generators.

GE said it expects to retain a stake of 19.9% in GE Healthcare once it is spun off. Jefferies analysts said the GE move raises pressure on Siemens to reduce its stake in Healthineers to under 50% to free up funds to invest in software.

“The question is: If I buy Siemens, do I want to also invest in Healthineers? Because if I wanted to, I could just invest in Healthineers,” which is publicly listed, said Vera Diehl,

fund manager at German asset-management firm Union Investment, which holds 1.2% of Siemens. “As a portfolio manager, I want to create my own portfolio of what types of businesses I invest in, not rely on the company to do that for me.”

Siemens’s Mr. Thomas said that unwinding stakes takes time, citing the need to transition intellectual property, data and various systems. He said Siemens was looking to completely unwind its stake in Siemens Energy and is open to considering more independence for Healthineers.

The shift at Siemens, a company that began in 1847 as a maker of telegraph machines, shows the benefits—as well as challenges—of the carve-out strategy, investors say.

“Siemens was a tanker, which was then transformed into a fleet of ships and high-speed boats, which it put on the water,” Ms. Diehl said. “It made the company more transparent and the investment story easier.”

While smaller, Siemens had competed with GE over the years as a maker of sophisticated industrial machinery. But inside the German company, GE had often been a source of inspiration and envy, top Siemens executives have said.

“GE was always the model, the benchmark,” said Manfred Hoefle, a Siemens watcher and former manager who spent 29 years at the company until 2005. “At Siemens you always had to justify yourself, and people would ask you, ‘Why don’t you do it like GE?’ ”

Siemens’s expansion, however, made the company inefficient and difficult to manage, investors and former executives say.

“At some point you saw that the synergies became very limited as complexity grew and grew,” Mr. Hoefle said. “If those responsible no longer understand the business, the company becomes only a portfolio managing center.”

A spokesman for Siemens said that the company has sought to create value by establishing focused, publicly listed companies as part of “the transformation of Siemens AG from a traditional industrial conglomerate to focused technology company.”

After taking over in 2013, then-CEO Joe Kaeser led an effort to refocus the sprawling conglomerate into a narrower selection of more-profitable units and to slash costs across the board, including thousands of job cuts. Siemens units got more autonomy to make decisions but also carried more responsibility for meeting financial targets.

The energy shake-up was triggered in part by worry over activist investors, Siemens executives said at the time. Back then, such investors, including some from the U.S., were pushing for boardroom changes in European companies like French beverage maker Pernod Ricard SA and German steel-to-elevator conglomerate Thyssenkrupp AG.

Shares in Siemens Healthineers have roughly doubled their value since the company was listed on the stock exchange, while the parent company is up 55% since then. Germany’s DAX index gained around 30% over the same period.

Siemens Energy shares are up 17% since their listing in September last year, underperforming the German blue-chip index’s 25% rise over the same period.

Write to Georgi Kantchev at georgi.kantchev@wsj.com