Permanent members of the Security Council (SC) have the right to veto Security Council resolutions. They don't have the power to veto resolutions by the General Assembly.

Generally, Security Council resolutions are much more important, because they have teeth. The Security Council has the "primary responsibility for the maintenance of international peace and security" (UN Charter Article 24). SC resolutions are also binding under Article 25, unlike General Assembly resolutions, which are non-binding "recommendations" (e.g. Articles 10 and 12). Further, only SC resolutions can authorize economic sanctions and uses of force (Chapter VII).

Under Article 4, admissions of new member states have to pass both the Security Council and the General Assembly, which means that it can be vetoed by the permanent members of the SC. This is the US can veto Palestine's UN membership requests, despite strong international support that's sufficient to pass GA resolutions.

However, one loophole of the Charter is that regime changes do not necessarily have to be endorsed by the Security Council. Thus, the General Assembly could not expel the Republic of China from the UN or to admit the PRC separately, but it could recognize the change of the legitimate government of China as a result of the Chinese Civil War.

What the General Assembly is essentially saying is that the ROC government no longer exists as a result of the civil war, and we have to recognize the new PRC government as the successor government. This is also what happened later, when the Soviet Union dissolved and Russia took its place in the Security Council.

General Assembly Resolution 1668 deemed the question of China's representation an "important question" under Article 18, which required a 2/3 vote in favor to recognize the PRC. Subsequently, General Assembly Resolution 2758 officially recognized the PRC as the legitimate government of China and rescinded any recognition of the ROC as a legitimate government.