There are many types of Superpowers such as nuclear, or conventional military, or financial/economic. Would not all three factors should be the deciding outcome who qualifies as the top superpower. IMO the USA does. However I'm asking this to settle an argument as one asked me to talk to Historians.
A superpower is defined as a power that has unparalleled levels of international influence on world affairs. This can be done through military power, financial power, as well as diplomatic influence.
Post WW2, the UN recognizes China, Russia, the US, France and the United Kingdom as great powers (aka the winners of WW2) and this is shown through P5 membership on the UN security council. Many people consider Japan and Germany to be super powers also in the military and economic sense, but not in diplomatic sense as they are both heavily influenced by America. However, great powers are not superpowers.
During the cold war, the USSR and USA were the two obvious super powers. The USA had the largest economy, the strongest navy by far, but lesser military and air force size and nuclear capacity than the USSR, but still enough to rival the them. The USA held influence over the majority of the UN security council, almost all of the capitalist world including Western Europe, some parts of Latin America, the British Commonwealth, and parts of East Asia (Japan, South Korea etc). The USSR held influence over China, Central and Eastern Europe, a good part of Latin America, Southeast Asia, and Africa.
After the fall of the USSR, their influence fell too low to be considered a true superpower, and the general consensus since then is that America is the dominant and only superpower in the world.