First some background answers I've written that will be helpful for setting the scene:

• The population of the Soviet Union grew rapidly from 1950 until 1990. However, after the collapse of the Soviet Union, the population of the former Soviet states stagnated and began to decline. Was the collapse of the union so serious that it caused that decline or is there something I'm missing?

• What was life like in the former Soviet Socialist Republics after the fall of the USSR? How did people survive in places like Kazakhstan when the supply lines collapsed? How did the transfer of governance proceed? What were those months like for ordinary citizens?

• Why was Poland's transition to capitalism so much more effective than Russia's in the 90s?

I point to these answers in particular because they get at some of what made the collapse of the Soviet Union different from Chinese liberalization. For all the economic changes that have taken place in the People's Republic of China since 1978 - and they are substantial - it is still a unified political entity under the control of the Chinese Communist Party.

In contrast, the Communist Party of the Soviet Union ceased to exist in 1991, and the Soviet Union (with its single economy) was replaced economically and politically with 15 new countries, which range from the developed (such as Estonia) to the desperately poor (such as Tajikistan). The space of the former Soviet Union was wracked by economic collapse (causing a depression far worse than the Great Depression experienced by the US in the 1930s), a complete political disintegration and restructuring, a demographic collapse, and a building of new economic and political institutions almost from scratch (which especially in a crisis is a far taller order than reforming and liberalizing existing institutions).

On top of that, Russia had to deal with dismantling a massive imperial legacy in a way China did not have to contend with. Something like at least 15% of Soviet GDP was spent on defense, maintaining a military that by many standards was the largest in the world and global in scope. Winding down these commitments, whether dismantling nuclear ICBMs, to transferring troops out of Berlin, to closing listening posts in Cuba or naval bases in Vietnam, cost money and were inherited burdens of a type the PRC simply does not have.

But finally: with all that said, I don't think it's fair to say "Russia's economy has stagnated since they ended communism". The Soviet economy collapsed starting in 1989, and Russia (along with the other former Soviet republics, and frankly all of the former Eastern Bloc) faced massive economic downturns in the early 1990s. For some republics, they never really pulled out of this hole. Russia, however, has, and has saw its GDP grow massively at the beginning of the 21st century, in no small part because of revenues from oil exports. Its economy grew at a much slower rate after the 2008 recession, and has mostly stagnated since 2014, but the growth rates of the first decade of the 2000s rivaled China's, and put the Russian "R" in the BRIC designation first coined by Jeffrey Sachs in 2003. Which is to say: Russia has some serious structural economic issues to this day (which are beyond the 20 year rule of discussion), and had a particularly hard economic transition in the 1990s. But its economy has moved past its Soviet levels, at least.

A final note is that China's staggering growth rates are in part because it started from a much lower level than the USSR, and was a much, much poorer and still majority-agricultural country when it started economic reforms in 1978, while the USSR by that time was a majority-urban and industrial economy, and so many of its issues are more of the "rust belt" type transitioning away from heavy industry. ETA - so to clarify, China's astounding growth rate (while it is astounding) is in part a function of it starting from such a low base: earning $11 after earning $10 the previous year is a 10% increase, while earning $101 after earning $100 is a 1% increase, despite the latter example having more money to start with. Russia by GDP per capita and GDP per capita PPP is still at a higher level than China, which is a bigger economy by virtue of having ten times as many people despite the lower per capita rates.

There are a lot of different angles that you can take with this, I'm going to take the economic angle since that's what I know well enough to talk about but other people could give equally valid answers that cover completely different ground.

First lets go over how industrialization works economically. Pre-industrial societies are generally dominated by agriculture and the average productivity of a pre-industrial peasant is pretty low. With even very simple industrial production you can often get a single factory worker to produce much much MUCH more than that peasant even after taking into account the costs of the industrial machinery. Since you don't have to pay workers that much more than the (very low) levels of pre-industrial peasant income to get them to leave their farms and go to work in your factory then you can make windfall profits. Those windfall profits can then be reinvested into more factory machinery et. an the whole thing explodes. For this to work, however, you need several things (this isn't by any means an exhaustive list but this post is getting long enough as it is):

1. A large number of workers who can be brought in to work at low wages (large low productivity farming populations are often the target for this).
2. Widespread literacy and basic education helps a lot.
3. Raw materials.
4. Markets to sell your finished goods to (since if you're a poor industrializing country you don't have much of a domestic market).
5. Good enough infrastructure to move good around.
6. A good source of suppliers for machine tools, components, etc.
7. Enough stability to not disrupt all of this with civil war or what have you.
8. Some kind of edge over the competition, since if dozens of countries are trying to do all of this at the same time some are going to do better than others. You can't have EVERYONE running low-wage export economies or nobody is going to be buying all of those exports.

Going down the list you can see that China had huge advantages over Russia in terms of being able to rapidly grow via basic industrialization:

1. When the Soviet Union fell, Russia was already pretty industrialized and had a much smaller body of poor rural farmers who could easy to tempted to get into industrial work for low wages. Russia was already fairly industrialized and at the time had VASTLY higher per capita income than China (Russia is still significantly richer than China per capita today) so Russia didn't have huge numbers of people who'd be willing to move to cities to work at factories for low wages that China did. Russia already had this kind of industrial boom all the way back before WW I with much more industrialization happening later so China playing catch-up had a vastly easier time experiencing rapid economic growth.
2. Communist countries (for all of the many many things that are wrong with them) are generally fairly good at basic education. So a wash here, but basic education did give China an edge over some countries with similar per capita GDP at the time.
3. Russia has plenty of raw materials but transporting raw materials over huge distances is very expensive, China is able to bring raw materials by sea (which is vastly cheaper) to its main industrial much easier than Russia can.
4. China was able to enter into enough free trade agreements to secure good markets for its goods. The main issue with Russia doing the same is the Dutch Disease. What this means is that if you export huge amounts of raw materials (specifically oil because of the huge amount of money involved but the same could apply to similar industries) then your currency appreciates. This makes exports more expensive and imports cheaper. So if you export enormous amounts of oil then it's just cheaper to import than to buy locally and very difficult to export anything else at competitive prices. The Dutch Disease often causes the non-oil parts of the economy to wither. We can see this in Russia and in pretty much every other major oil exporter. Oil can bring in huge amounts of money in the short term, but it often crowds out other kinds of economic development and can cause serious economic problems in the long run. This is why Norway, for example, tries to save instead of spend a big chunk of its oil earnings so that it can keep that huge inflow of cash from distorting its economy too badly.
5. Pre-reform China didn't have very good infrastructure but the sheer enormous size of Russia makes setting up good infrastructure very difficult. Also China's industrial areas are mostly right along the coast which makes transportation much easier and bad infrastructure (at the time) in the interior not matter as much.
6. Having Japan right next door as a source of machine tools helped a lot as does China's sheer size. If you're running a factory in China and need a certain component then there are huge numbers of suppliers available locally. Of course this wasn't true at the start but this has helped China to keep on trucking for a long time with its economic growth. It's just easier to set up a new factory in an area where you know you can find many different suppliers of the components you need and many workers who already know how to do the processes you need to be done.
7. The fall of the Soviet Union was much more sudden than China's reforms. The shock of moving off of a command economy so suddenly was very disruptive in Russia.
8. China's edge here (aside from being VASTLY VASTLY poorer per capita than Russia at the start of this period which made growth incredibly easier, in many ways China was only able to grow so fast because Mao had set them back so far economically that playing catch-up was easier it's so easy to overstate China's economic miracle, China still has a lower GDP per capita by PPP than Thailand, Serbia, or the Dominican Republic and nobody calls any of those countries economic miracles despite all of them being richer than China) is its sheer size. Western companies have been drooling over the idea of "if every Chinese person bought just one of my product I'd be so damn rich" which made it easier for China to cut deals with foreign companies. Even when China didn't have much of a domestic market for foreign companies the potential due to its immense population attracted a lot of people. Also imagine that you're a western discount retailer and you want to import a lot of cheap stuff to stock your shelves with. The sheer size of China makes it easier to just do a lot of stuff in one country and deal with the same people, the same laws, and the same language with huge numbers of suppliers to choose from rather than having to deal with a dozen countries offering products at similar prices.

So because of all of this, China has been able to grow rapidly. But will it be able to keep on growing? If Russia has a bad case of the Dutch Disease than China seems to be falling face-first into the middle income trap.

If you look at the advantages China has been able to enjoy a lot of them stem from being able to draw huge numbers of economically unproductive farmers out of rural areas who are willing to work for very low wages. That's drying up. Chinese wages are far higher than they used to be and there really aren't huge numbers of young rural farms who can be brought to the cities for low wages. Now while that is obviously a very good thing for average Chinese people it means that China is going to have a lot of problems continuing to grow.

Other countries such as Indonesia to give one of many many examples are now starting to undercut China since the wages are lower there. China still has an edge because it's simply a lot easier to find the right suppliers, workers with the right skills, etc. etc. in China but how low will that advantage last with basic industrialization booming elsewhere. If Chinese products are more expensive because Chinese wages are higher will people really pay a premium for things made in China instead of things made in Sri Lanka?

Now that doesn't mean that China will crash, just that it'll start to stagnate. It has a much bigger domestic market than it used to but the middle income trap will hit it hard. It's easier to expand when the main edge you have is cheap labor but if you expand enough that your labor isn't cheap anymore then what then?

Korea was able to avoid the middle income trap because people will pay more money for a Korean car or cell phone than a Chinese one and its cultural cachet has allowed it to bring in money in ways aside from industry. These days Japan is huge in machine tools and is doing OK even as a lot of its consumer brands are declining. But due to the dead weight of the CCP, China doesn't do well in terms of cultural exports (just look at what's happened to the Hong Kong film scene), or attract much tourism compared to the huge size of its economy, etc. etc.

China will continue to be a huge economy but you'll be seeing less and less "Made in China" in Walmart in the coming years due to simple costs which will take a big bite out of its growth rate.

Again note that I haven't really talked about government policy or organization pretty much at all. There's another huge post there covering a lot of additional ground.