Last summer, when Jeff Blau, chief executive of Related Cos., was approached by a young vice president with what he saw as a great buying opportunity, no one at the company thought it would trigger one of the fiercest commercial real-estate brawls in years.

The battle, which is headed for a showdown this week, pits Related, controlled by billionaire Miami Dolphins-owner Stephen Ross, against the Portnoy family of Boston, which controls a property empire worth more than $20 billion. It also shines a spotlight on the world of real-estate investment trusts that are run by external management companies.

It was one of these REITs that caught Related's eye: CommonWealth REIT, CWH -0.55%a Newton, Mass.-based landlord that owns more than 300 U.S. office buildings.

Last summer, Related officials realized CommonWealth's shares were trading at a steep discount, in part, it said, because investors and analysts didn't like that it was managed by an outside company. The Portnoy family, which controls CommonWealth, also owns the outside company, Reit Management & Research LLC.

"My initial response was, I don't believe it," Mr. Blau said in an interview, describing his surprise at how undervalued the stock was. "It's a public company. The markets are pretty efficient.…[The vice president] came back about two weeks later and said, 'No, I'm telling you…the assets are worth much more than the stock price.'"

In January, Related and a partner, hedge fund Corvex Management LP, started amassing what eventually would rise to a 9.6% stake in CommonWealth in a bid to shake up management or gain control of the company. Related has said in public filings that 70% of CommonWealth's shareholders had voted by June in favor of a measure to oust the company's board.

The Portnoys have been resisting the effort, throwing up numerous legal roadblocks. "They're using the cloak of corporate governance when they're really wolves in sheep's clothing," said Adam Portnoy, president of CommonWealth, referring to Related. "We believe Corvex and Related are trying to seize control of this company, without paying for it, in order to misuse CommonWealth."

On Friday, an arbitration panel will hold a hearing on one of CommonWealth's strategies to resist takeover, which could go a long way toward determining the winner. The issue before the panel is the technical question of whether CommonWealth's board, controlled by the Portnoys, had the right to change its bylaws to prevent all but large, long-term shareholders from calling for its ouster.

But the battle is being closely watched because it has amplified criticism of so-called externally managed REITs. Unlike most REITs, which employ their own management team, these companies pay outside companies hefty fees to manage operations.

For example, RMR's fees from managing CommonWealth have risen to $69.8 million in 2012 from $60.2 million in 2007, according to the company. Over the same period, CommonWealth's total stock price return has underperformed the Nareit Office Index, a common benchmark of office landlords, by 36%, according to Green Street Advisors.

Externally managed REITs have long come under fire for alleged conflicts of interest between the companies and the management firms they hire. The Portnoy family controls four more of this type of REIT besides CommonWealth, which it founded in 1986.

In the case of CommonWealth, a group of dissident shareholders led by Related and Corvex point out that RMR gets paid fees based on much property the REIT owns, regardless of whether the buildings are profitable. That has led to bad investments for CommonWealth that have earned more fees for RMR nonetheless, they say.

The dissidents also point to CommonWealth's decision this spring to reinstate a director after shareholders voted him off the board. "In all my experience doing this, I've never seen a company's managers have such blatant disregard for shareholders before," says Keith Meister, founder and managing partner of Corvex, and a former deputy to activist investor Carl Icahn.

CommonWealth's board and RMR say the external management structure saves investors money by sharing the cost of accounting, engineering and planning between CommonWealth and the four other REITs that RMR manages.

RMR blames the company's underperformance in the stock market on a long, painful transition the company has launched from owning mostly suburban office buildings to owning mostly urban ones.

"Commonwealth has always been—and continues to be—committed to doing what's in the best interest of shareholders," says Mr. Portnoy, who along with his father Barry, runs RMR and is on the board of the REIT.

The takeover effort comes as office-building values are rising as a recovering economy drives rents and occupancies higher. Investors also are bidding up prices because returns on real estate are higher than what they would get from bonds in the current low interest-rate climate.

Currently, there are about 18 externally managed REITs in the U.S., excluding REITs that invest in mortgage-backed securities, according to Green Street. But recently, the structure has begun to spring up again, including in the mortgage REIT sector and the nascent industry of REITs that focus on buying and renting out single-family homes.

"These guys are the dinosaurs of this industry," Mr. Sullivan says. "It's a company that's been providing terrible total return to their investors. There are incentives to make the company bigger, whether or not that's good for shareholders."

As evidence of a conflict, Related executives point to CommonWealth investments like Heritage Landing. In 2004, the company paid about $61 million for the early 1980s-built office complex in Quincy, Mass., a middle-class suburb about 7 miles south of Boston.

The complex's only tenant, State Street Corp., STT +1.69%left in 2010 and it sat vacant since then. CommonWealth sold the property earlier this year at a loss, for $16.3 million, but RMR continued to collect fees from the property as long as CommonWealth owned it, critics say.

The younger Mr. Portnoy counters that the Quincy example "demonstrates why we wanted to move away from suburban office" properties. "This is one building…that didn't work out," Mr. Portnoy said. "For every one of these buildings like Quincy, there are numerous examples of buildings that created significant shareholder value."