The overarching motivations for the oil embargo were relatively simple: many OPEC members were still vehemently opposed to Israel, and viewed oil as a potent weapon. They viewed their ability to exercise dominance in the world economy through the use of oil in that way as a large and substantial factor for their growing geopolitical clout, and this was as good a time as any to demonstrate it.

When you get down to the individual level, it gets a little more interesting. For example, why was it so much more effective than in 1967? In part, this was because of the development of the oil business in places like Saudi Arabia, which I want to focus on. In Saudi Arabia's case, it ended the oil embargo in 1967 almost immediately following the September Khartoum Resolution, and did not strictly or widely enforce it, due to more moderate politics at the time and also a different structure governing its oil production. Aramco, the main producer there, was formed in 1944 as a successor to the California Arab Standard Oil Company, which itself was a subsidiary to Standard Oil of California. Saudi Arabia saw significant benefits from the increase in oil production as this American-rooted company started up, but eventually the balance began to shift.

While his father, King Saud bin Abdulaziz, had preferred not to use oil as a weapon, King Faisal eventually came around. Faisal became king in 1964, but in the early years, continued to adhere to his father's statement that "oil and politics should not be mixed". Aramco was, after all, still sharing profits with Saudi Arabia, and even making more profits than it was. This became devastatingly apparent in 1954, where Aramco made more money on Saudi oil than Saudi Arabia did during an oil glut and drop in prices. This state of affairs is part of what prompted the founding of OPEC to begin with.

In 1968, i.e. notably right after the 1967 war, Faisal began to make changes himself. He revised the agreement with Aramco, raising the kingdom's income from oil exports by over 50%. Notably, he would later go on to get Aramco (perhaps in part through the pressure of the oil embargo) to become majority-owned by Saudi Arabia.

But there was another reason Saudi Arabia may have gone along with this embargo, and it was more personal. First, Faisal and Kissinger got into a disagreement when Kissinger asked him to condemn Egypt and Syria for attacking Israel unprovoked. Faisal refused, supported the two, and called on Kissinger to force Israel to leave Sinai, Gaza, the West Bank, and the Golan Heights instead. OPEC met and decided to cut supplies and raise prices, but President Nixon assured Faisal that the US would not show favoritism in the war, perhaps to forestall further pressure or an outright embargo. But Nixon would go on to give aid to Israel, through aid shipments especially (which the Soviets were providing to the Arab countries as well), and Faisal felt that this was a personal betrayal of Nixon's promise. That, coupled with wide publicity for the assistance, led Saudi Arabia to begin the embargo unilaterally, and other OPEC members then joined.

Faisal had warned the US this would occur, in a roundabout way. He sent a letter to the United States calling on it to stop aiding Israel as the tide shifted towards its favor, and said relations could be "lukewarm" if it did not. Thus when the US went ahead with an aid package, it seemed possible that Faisal would react with an embargo, as he certainly did. The US stuck to its guns, preferring to continue ensuring Israel could beat the Soviet-allied Arab states and secure a favorable ceasefire following their attack, but the production cuts (more even than the embargo itself) took a massive toll, as prices tripled. The production cuts hammered the entire global market for oil, far more than a unilateral embargo on the US. After all, only 12 percent of US oil consumption came from crude oil or refined products from the Arab world. An embargo alone would not do nearly as much as production cuts would, because production cuts would raise prices on oil imported from everywhere, which also made a significant difference in 1973 versus 1967.

There's a lot more that could be said, but I hope this gives you a good rundown!