(This is a two-part answer that may be edited later. All sources are provided in the reply at bottom. Mahalo for reading.)

The short answer is that it was a complicated mix of money, special interests, cultural identity and public desire for political power that ultimately lead to statehood for Hawai’i.

In Last Among Equals: Hawaiian Statehood and American Politics, Roger Bell wrote that Hawai’i statehood was a giant headache for everyone thinking about it:

Annexation was an agonizing question for Congress. No less complex were the resulting issues of Hawaii’s political status and the terms under which it should be governed. In part, such problems derived from a belief in Washington that a strategic outpost like Hawaii should be tightly controlled, especially one whose population was primarily 39 percent “alien.” But they were also a product of pressure from white settlers who comprised less than 20 percent of the islands’ population and were anxious that territorial status should confirm, not threaten, their established authority. In particular, they wanted territorial rule to ensure physical and economic protection by the United States, even if this brought the islands under immigration laws which restricted the access of planters to Asian labor. The rights and interests of Hawaii’s Caucasian minority could be best protected, its members argued, if Washington had ultimate authority over government in the islands. This view subsided very slowly. But by the 1930s, in the face of attacks by Congress against “King Sugar,” it was challenged from within the haole (white) group. Many of those who had once championed territorial rule now questioned its capacity to protect their interests. They turned, instead, to statehood. (1)

Public calls were already being made to become a state. A joint resolution passed in 1903, with bipartisan support by the territorial legislature and signed by territory governor Sandford B. Dole, asked outright for statehood. (2) But Congress preferred to put off the annexation question and kept kicking the can down the road until events forced their hand.

Between the eras of territory and statehood, Hawai’i was a major player in world commerce. Besides being a well-placed midway geographical port for global shipping between Asia and the Americas, Hawai’i was a strong agricultural center. It grew coffee, a variety of raw fruits and vegetables, processed sugar cane into refined sugar, raised livestock, grew industrial hemp for rope, etc. Demand for these goods was high, and people who owned the plantations and ranches these products came from became very wealthy. The majority of owners of these plantations were also white, and so a new class of wealthy white landed gentry came of age to grow very powerful in Hawai’i politics. The plantations merged with other white-owned Hawai’i businesses and grew into a conglomerate known locally as the “Big Five”; five financial entities that controlled giant swaths of land, economic resources and money inside Hawai’i.

In 1903, Hawai’i Attorney General Edmund Dole described the Big Five as “a government in this Territory which is centralized to an extent unknown in the United States, and probably almost as centralized as it was in France under Louis the Sixteenth.” (3) That was an incredible amount of power to wield, and keeping Hawai’i as a territory was seen as a way to keep that power. And the Big Five favored being a U.S. territory with all the benefits of being the new Hawaiian royalty while enjoying the protection of the American government, until it wasn’t.

Meanwhile, immigrant workers from other countries were brought in as physical labor for the Big Five’s businesses and plantations. They and found they had no real labor rights in Hawai’i, and endured very harsh working conditions, extremely low pay, and subtle and overt racism from a newly established class system of haves and have-nots. Frustration built up over their continued mistreatment by the dominant Big Five employers, leading to a push and rise of all-encompasing unionization of the islands in the 20s, 30s and 40s.

In Fighting in Paradise: Labor Unions, Racism, and Communists in the Making of Modern Hawaii, Gerald Horne interviewed former sugar executive Howard Babbitt about his thoughts of what became known as the Sugar Strike of September 1, 1946. My added comments are highlighted in italics:

Howard Babbitt knew the score. This executive of C. Brewer (a Big Five company name) was living large in postwar Hawai‘i, but he knew the same did not hold true for those he employed. He realized in particular that conditions were harsh for the wartime working class in the archipelago. “[They] worked long hours,” Babbitt recalled years later, “10 and 12 hours a day, and under blackout conditions that were pretty disagreeable. The mills were all blacked out[,] so that it was stifling hot.” That was one of the many reasons why he thought that unionization spread like a prairie fire throughout the islands, transforming the politics of Hawai‘i in the process. These onerous working conditions were “one of the reasons that the men were so easy to organize, unionize after the war,” he observed. “[T]hey just have been working so long and so hard that they wanted a vacation. A strike, in a large part, was a vacation to them[;] most of them had pretty large savings because they couldn’t spend money during the war (World War II).” (4)

Unions became a way to push against the current power structure of Hawai’i and force change that improved people’s lives. Horne writes at length on how unions shaped the way that Hawaiians began to perceive themselves, not as outsiders but as part of a valued group, and showed others like the Big Five and other ruling elites that effective change could be made. And as more and more people pushed against the idea of the ruling elites controlling everyone in a mere territory, and that statehood would lead to eventual self-determination free of corporate influence, the ruling elites started advocated for statehood as a different, yet effective way to maintain their power in self-preservation.

The main difference between the territories boils down to how they became part of the United States and therefore how these territories interacted with and viewed themselves vis-a-vis the United States government.

Although Hawaii, Guam, and Puerto Rico all became part of the United States around the same time (1898 & 1899), the circumstances were not the same for all three territories. The annexation of Hawaii was a fraught political matter that played out over nearly five years. Throughout the latter half of the 19th century, American sugar planters had been gaining influence and power and had been pushing the country (as Hawaii was an independent nation at the time) towards closer ties with America. In January 1893, a group of American sugar planters overthrew Queen Liliuokalani after she announced that she was going to replace the existing constitution (which limited voting rights for native Hawaiians and put power in the hands of American planters, who were a small minority of the country) with a new one, restoring voting rights to native Hawaiians. These planters, led by Sanford Dole, formed a provisional government with the express intention of being annexed by the United States. By February, the Harrison administration had signed a treaty of annexation and submitted it to the Senate. However, Harrison was a lame duck president and the incoming president, Grover Cleveland, made it clear that he wanted to look at the issue during his administration, so the Senate agreed to defer the vote until he took office.

Although the American sugar planters and the Harrison administration were in favor of annexation, this was not a universal sentiment. Up until this time, the United States had steadily expanded, but only ever on the continent. Alaska had been purchased in 1867, but that was a sparsely populated area, and again, had been purchased from a European country, not annexed. Annexing Hawaii would turn the United States from a continental power to an overseas one and potentially bringing it into foreign entanglements, which it had historically tried to avoid. The United States had historically supported an independent Hawaii and annexing a territory that had just undergone what many saw as a dishonorable coup was distasteful to a large portion of the population. The U.S. ambassador to Hawaii had sent marines onshore during the coup (the US had a base at Pearl Harbor even then) and the presence of US troops had given many the impression that the US was invading, or that the US government had sanctioned the use of force. Native Hawaiians overwhelmingly wanted their queen and self-government back, and many in the US found it difficult to justify annexing an independent, sovereign nation whose population was strongly against it.

In the end, Cleveland withdrew the bill for annexation from the Senate before it could be taken to a vote and in December 1893, delivered a message to Congress that he would not pursue Hawaiian annexation any further and that he supported a restoration of the monarchy. Unfortunately for the Hawaiian queen, his words were not backed by concrete action, as Cleveland refused to send in troops to restore the monarchy and Hawaii remained an independent republic with Sanford Dole as president. In 1897, William McKinley became president. A far more ardent expansionist than Cleveland, he submitted a treaty of annexation to the Senate in June. It encountered a fair amount of resistance and so was abandoned in March 1898 to be left without a vote, but not withdrawn.

In April 1898, the Spanish-American war was declared and opposition to Hawaiian annexation dissipated. In July, the Senate voted to annex Hawaii, a process that was noted as being requested by the Hawaiian government and Hawaii became an incorporated territory of the United States.

Unlike Hawaii, Guam and Puerto Rico became part of the United States as part of the Treaty of Paris in 1899, when Spain ceded them (along with the Philippines) to the United States. These were the first territories that the United States had ever won from a European power in war and it was never clear what the United States was going to do with these territories. They wanted the Spanish out, which they had achieved, but these were majority non-white, non English-speaking territories that had been gained in war and were more like colonies than anything else. The idea of "unincorporated" territories came into place as the government how the US would govern these territories and how much the Constitution would apply and there were a series of court cases as the legal system attempted to figure it all out. The Philippines eventually became independent, but clearly Puerto Rico and Guam remain part of the United States today, with the same questions about their status and whether or not they should become states.

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Sources:

Expansionists of 1898 by Jules Pratt

Empire Can Wait by Thomas Osborne

Island World by Gary Okihiro

Aloha Betrayed by Noenoe Silva

The United States and the Hawaiian Kingdom by Merze Tate