Bangladesh built Sushil Kumar Sarkar a cyclone-resistant home on his land near the Bay of Bengal as part of a government-funded program to protect the region from rising storm intensity that scientists say is a result of climate change.

Fearing it could collapse at any time, Mr. Sarkar refuses to live in it. “This house isn’t fit for my cows, let alone my family,” he said, standing in front of the dark and damp one-room building.

Far away in Paris, rich and poor countries are negotiating a global climate-change agreement. Strands of a deal began to emerge on Tuesday, but divisions remained on the two most contentious issues: Who will help developing countries pay for less-polluting energy generation and adapt to rising temperatures; and whether emerging economies take on larger responsibilities in the broader fight against global warming.

At the heart of the talks is a debate over how the world’s wealthiest nations will pay to help people like Mr. Sarkar in the world’s poorest cope with the effects of climate change, such as rising sea levels and more frequent and powerful storms.

The sums involved are huge. Wealthy nations have pledged to channel at least $100 billion a year to poorer ones by 2020—and possibly more after that—to pay for a vast array of infrastructure, from cyclone-resistant housing to wind turbines to farms that can flourish in salty soil.

Developing countries say donor nations should ease regulations on how the money is spent. But the developed world is wary, and Mr. Sarkar’s house highlights why: Rich nations fear that weak government institutions, lack of resources and corruption in poor countries mean climate funds will be wasted.

Before the money can flow, wealthy countries say, the developing world must commit to follow detailed regulations to ensure that projects are well-executed and money isn’t lost to corruption.

“We don’t hand over $100 billion to whoever asks in developing countries,” said Jochen Flasbarth, Germany’s state secretary for environment, adding that “those countries with low or with no corruption do have better access than countries known for a lot of corruption.”

Poorer nations say they don’t have time to navigate the rich world’s maze of red tape when faced with what they call the emergency of global warming. At the Paris summit, they are demanding more control over how the money gets spent.

“It should not be conditional. It should not be earmarked,” said Nozipho Mxakato-Diseko, the South African diplomat who is representing a group of more than 100 developing nations in the talks, “because we know what we’re dealing with in our countries. We know better.”

Rich and poor hope to strike a deal in Paris. Countries around the world are proposing to limit their greenhouse-gas emissions, even though most of the warming that has happened since the dawn of the industrial age, scientists say, is the result of emissions from wealthy nations. In return, poorer countries say, the developed world must make firm commitments at the summit to help them pay the bill.

To give developing nations more control over climate funds, wealthy ones are exploring new ways of delivering aid. The U.S., Europe and others have pledged $10 billion for the Green Climate Fund, which is geared toward allowing poor countries to propose and manage large climate-change projects—provided that they have strong accounting practices, protect whistleblowers and meet a long list of other criteria.

The Green Climate Fund tentatively approved its first eight projects in November, though officials say it may be a year before money actually flows.

Despite the fund’s mission, developing nations say bureaucracy is shaping up to be a major challenge to accessing money. The fund’s decision to allow Deutsche Bank AG to manage projects stoked their suspicions that wealthy nations preferred to channel the climate fund’s money through their own financial institutions. A Deutsche Bank spokesman said it was an honor for the bank to work with the fund and declined to comment further.

Officials say getting institutions from the poorest nations through the rigorous screening process for handling the fund’s money is going to be difficult.

“The donors, of course, don’t want to lose their money,” said Jozef Buys, Belgium’s representative on the fund’s board.

Development money in some other nations vulnerable to climate change has recently gotten tied up in high-profile corruption scandals. In the Philippines, a businesswoman was convicted this year of conspiring with government officials to steal tens of millions of dollars dedicated for local infrastructure projects.

In the Maldives, the government’s auditor uncovered an alleged scheme that allowed government officials to embezzle $1.6 million of international donations that were supposed to help the low-lying, Indian Ocean archipelago to recover from the 2004 tsunami. The officials lost their jobs, but they haven’t been prosecuted.

Ahmed Sareer, the Maldives ambassador to the United Nations, said the country managed the recovery from the 2004 tsunami well, despite the scandal. “Maldives has taken a very serious position on governance and accountability,” Mr. Sareer said.

The Maldives, the Philippines and Bangladesh have had success working with international donors on climate projects. The Green Climate Fund awarded one of the projects announced in November to the Maldives, though it will be managed by the United Nations Development Program, not by the Maldives itself. Bangladesh also won financing for a project from the fund, to be managed by Germany’s development bank.

In Bangladesh, wealthy donor countries set up a climate-finance fund in 2010 that was supposed to give more power to the government over aid decisions. Though initially managed by the World Bank, the goal was to establish a secretariat for the fund the Bangladeshi government would run.

But last year, the donors and the World Bank decided to shut it early, with less than half of the money approved for projects, amid persistent delays and concerns about monitoring the fund’s operations. Staff hired to run the Bangladeshi secretariat have been let go, ending hopes for now that it would become an enduring institution to spend climate-change money.

“It is now clear that (the fund) will not be a transformational example of a multidonor mechanism for providing support in alignment with government plans,” said a report published in June by the U.K. Department for International Development.

A World Bank spokeswoman said project implementation under the fund sped up in 2014 after a slow start, which she blamed on coordination issues between the government, donor countries and the World Bank. She said the World Bank had “set up infrastructure” for the secretariat, but it was now up to the government to manage it. “It takes time to put in place technical and fiduciary safeguards for projects.”

A fund established by the Bangladeshi government using its own money has been more active. But the projects it financed, such as the cyclone shelter built for Mr. Sarkar, the Bangladeshi farmer, have been undermined by lack of resources and oversight, say Bangladeshi officials and nonprofit groups.

“We’re given money for implementation but there is no budget for maintenance and monitoring afterwards,” said Khandoker Khalequzzaman, chief engineer of the Water Development Board, a Bangladeshi government agency responsible for many of the country’s climate-change projects.

Mr. Sarkar’s house is one of more than 2,000 similarly designed houses built by Bangladesh’s Department of Disaster Management at a cost of nearly $3 million between 2011 and 2013.

Local residents say the houses were initially built without walls: Government officials argued that the “open” design would help make the houses cyclone proof. After an outcry from human-rights groups and civil society organizations, walls were added more than a year later, locals say. People in at least four villages, visited by a Wall Street Journal reporter, said the houses are still mostly unfit for human habitation.

Riaz Ahmed, director general of the Department of Disaster Management, said some houses weren’t built properly “due to lack of monitoring at local level.”

“We are investigating and will take action, including confiscation of contractors’ security deposits and blacklisting them if necessary,” he said.

The Bangladeshi government has won plaudits on the global stage for adopting a climate change policy as long ago as 2009, among the first developing nations to do so. In September, the U.N. Environment Program declared Prime Minister Sheikh Hasina one of the winners of the United Nations Champions of the Earth award in recognition of Bangladesh’s initiatives to address climate change.

Now, the government needs to improve its ability to execute projects on the ground, says Atiq Rahman, a climate scientist and director of the Bangladesh Center for Advanced Studies, a think tank focused on environmental issues.

“We can do better governance,” he said. “We can do better management—every penny must be accounted for.”