I would say economically and politically PRC had more to offer. during the recognition of PRC as China in the 70s, the PRC just had more to offer to the western world. While ROC was an Part of the allies in WWII, the Cold War during that time and the war in Vietnam kind of made the PRC a nation that had to be treated with care. One wrong move and it will not be pretty. As PRC showed the world during the Korean War, it had the manpower to push back the UN forces. But China played the ace card by officially “splitting” from the Soviet Union. Also during this time ROC did not recognized the independence of Mongolia, which slowly shifted the western support for ROC. Therefore Nixon the president of the USA at the time and other UN nations voted for PRC. China and Taiwan did not want to take military actions, and both PRC and ROC was pushing the one China policy which dismantled the possibility of two Chinas like the current North and South Korean and the former North and South Vietnam. so it was a mixture of the interest of the western worlds amidst a Cold War, and it was because both China and Taiwan itself was pushing a One-China policy that all of China should be under one rule, leaving the possibility of two chinas off the table. Since then Taiwan has relaxed its one China policy so that they could be accepted as a sovereign nation in the UN, but still without success. With China becoming an economical and diplomatic powerhouse, who knows if the UN will ever allow two chinas. Back then and even now it is decided by the interest of the UN nations.