There are some absolute factors, and some relative factors that make Russia a power (you can argue whether it's a Great Power or Regional Power or whatever, but not a superpower) while the USSR was a superpower.

A big difference is in military size and the ability to project military force. The Soviet military even in its last years (when morale, order and budgets were crumbling) was something on the scale of 5 million personnel, and tens of thousands of nuclear warheads, tens of thousands of battle tanks, bombers and fighter aircraft which were considered competitive with their Western counterparts. Even the Soviet Navy, despite having beefed up ship numbers (over a thousand) from not retiring obsolete ships, was still able to put a formidable number of modern ships to sea: aircraft carriers, ballistic missile submarines, nuclear attack submarines, as well as a variety of modern destroyers and frigates.

And the Soviet military was very much not just based in the USSR. It was part of a larger military alliance (the Warsaw Pact), that included Czechoslovakia, Poland, East Germany, Romania, Hungary and Bulgaria (as well as Albania to 1968). The Soviets not only stationed substantial numbers of troops in these countries, but these countries themselves provided large militaries (much larger than the current countries have) that were part of the Soviet alliance system.

And that's not all: the USSR had troops stationed in other friendly socialist countries. Perhaps most notoriously Afghanistan after 1979, but also (much more peacefully) in Soviet military bases in Mongolia, Vietnam, Cuba, Ethiopia and South Yemen as late as 1989. And that isn't counting the countries that were not technically Marxist-Leninist like these others, but were at various points on good political terms with the USSR, and received Soviet aid and thousands of military and civil advisors. This number at various points included China, India, Indonesia, Egypt, Algeria, Libya, Syria, Iraq and Guinea. And that doesn't include the numerous Marxist-Leninist parties and revolutionary/insurgent groups that received support and training from Soviet authorities or Soviet allies.

Russia just doesn't have this. It inherited most of the Soviet military, but not all, and what it possessed was much reduced in size and potency over the next decade or so. Some of this was from honoring arms control treaties that were signed in the last years of the Cold War, such as the Conventional Forces in Europe Treaty, the Intermediate Range Nuclear Forces Treaty, and the Strategic Arms Reduction Treaties. But this was also because the Russian government could not and would not continue to invest in the massive Soviet military and arms industry, which made up perhaps 15 to 20% of the total Soviet economy. The size of the Russian military is far smaller than the Soviet military was even in its last years, and the arms industry had a good decade turbulence within a much wider period of social, political and economic turbulence - making slightly updated versions of Soviet era weapons at a vastly slower pace and usually for foreign clients. It was well into the 21st century before many new weapons systems began to be developed and produced, and at much slower rates and smaller amounts than in Soviet times (the fact that more modern weapons are much more complicated and expensive to develop didn't help).

But there are also relative differences. The USSR was the third largest country by population at its fall: China and India alone were larger. It also spent much of the Cold War being one of the biggest economies in the world, not so much for it's wealth (on per capita terms it was similar to Argentina or Mexico) as for its size from its large population. Even so its economy at its best was about a third the size of the US, although I should note that the USSR didn't use prices like a market economy and so estimates of Soviet GDP could vary quite a bit between the economic specialists in the West who tried to compare it to other countries.

After the Second World War, even with the massive devastation the USSR suffered, it was therefore just still that much bigger than most other economies, except the US (which in 1945 was something like a good half of the world's industrial output). Germany and Japan were physically devastated, and France and Britain largely broke, with much of the world still very agricultural and poor, or emerging from colonialism or recovering from war devastation, or all three. The USSR had some of the highest annual economic growth rates of any country in this period as well, which made it something of a model for developing countries. However, as the decades went on, the Soviet economy grew at ever smaller rates (but it still grew), and the gap did not close with more advanced Western economies, which moved into post-industrial information and high tech industries, while the USSR had trouble making such leaps. It began to be surpassed by countries like Japan, and was just not moving ahead.

The Soviet breakup not only broke up this single economic unit (Russia being 3/4 of Soviet territory but only 1/2 of its population, with much of the best farmland, oil resources, and advanced industries in other republics), but all 15 of the successor states went through massive turbulence in the switch from centralized to market economies. GDP plunged massively - Ukraine and Russia saw their GDP fall by half in the 1990s). Life expectancies crashed, and populations shrank in many republics. Immigration saw millions move between the republics, and quite a few of the most educated and most skilled leaving the former USSR forever. For Russia the economic turnaround didn't come until 2000 and the Russian economy didn't reach its pre-1991 size until the middle of the 2000s. It also became extremely dependent on oil and gas exports, and for a variety of factors that I can't get into here because of being after 2002 its economy just didn't grow very fast since 2008. And that's all when the Chinese economy roared ahead by something averaging 10% a year from 1989 basically until the past few years.

So: Russia is smaller in terms of population and economy than the USSR, and fields a much smaller military on a much smaller budget with less military allies and less means of projecting its military around the world. It is not the heart of an alternate political-economic system championed by allies, admired by friendly countries, and which supports major political parties and revolutionary movements elsewhere. It's a much more "regular" country, albeit one that probably still punches above its size because of its military and arms industry (and its massive oil and gas exports). On top of this, the past few decades of population and economic growth in other countries and parts of the world just have not been matched by the former Soviet Union, which means that in relative terms it has lost a preeminent place. Where in 1989 the USSR was a superpower and China a junior aspiring power, the relative situation has reversed in some 30 odd years.