Of these three empires, I would argue that Japan adapted the best to Western ways, that Russia was second, and that China did the worst job of adapting. It may be that China is overtaking Russia in this regard today, but it did not do so in the past.
Japan did by far the best job of adapting to Western ways. This was a country that was, until Perry “opened” it, completely detached from the modern Western world. By 1895, Japan was strong enough to defeat China in a war. By 1905, it was able to defeat Russia. Both of these countries were much larger than Japan and had more resources and yet Japan defeated them. By the 1930s, Japan’s military might was arguably on par with that of any country in the world other than the US. This shows that Japan adapted very well to Western ways and was able to become the equal of the Western nations.
Neither China nor Russia did as well in this regard. Russia did better than China in that it was able to become much more industrialized and to have much more military power at all points in modern history. Of course, Russia was more exposed to Western ideas and therefore had a greater chance to absorb them. China adapted terribly. It has only modernized its economy and, to some degree, its society in the last 20 or 30 years.
So why was this? It is impossible to know for sure. The most logical speculation that I have heard is that Japan was small and vulnerable and therefore knew that it had to change. Russia and China were large enough and dominant enough in their own regions to feel that they had no need to change. Therefore, Japan was much more open to Western ideas and adapted to them more easily.