Britain and Japan, both islands off the coast of large landmasses.
Britain endlessly interferes with European politics to ensure that no European force comes to dominate the continent and power is decentralised. Europe is constantly at war for 1000 years but becomes the scientific and technological leader of the planet.
Japan retreats into itself and allows a series Imperial dynasties to rule China as a whole. China is not endlessly peaceful but does have a large overall national identity.
I have an idea why this happened - the Mongols - could this have turned out differently?
Perhaps the Mongols go West, and their invasion of Japan in OTL becomes the invasion of Britian, with similar results. In the West an insular Britain off the coast of a backwards German (Mongol originated) Empire
and in the East a liberal, acquisitive forward looking Japanese state which interferes with the independent states of China, and begins to colonise the New World the way Britain did?
Could we reach the 20thC with a mirror image set of World Wars originated by the states in the East over their colonies in the West?
Generally speaking, China remained far more consolidated than Japan for more than 3000 years. There were times when the former was extremely fragmented, most notably during the Sixteen Kingdoms Period (304-439), along with the Northern and Southern Dynasties (420-589), but Japan remained relatively decentralized until the 6th century, so it wouldn't have even been able to contemplate an incursion into China. The last major period of division within China was during the Five Dynasties and Ten Kingdoms (907-960), but Japan had its own set of political issues as the court began to gradually gain influence, so a planned invasion would have been out of the question.
The gradual transition of power from the monarchy to the shogunate in power, along with China's relative stability at the time, also meant that Japan was unable to consider any form of expansion from around 1000-1585, especially during the Sengoku Period (1467-1600). In fact, Hideyoshi's invasion of Korea (1592-8) was a complete disaster mostly due to complex logistical issues, along with China's willingness to aid its vassal, so even a tentative incursion into China at the time would lead to an even bigger catastrophe. The aborted invasion was also one of the reasons why Japan decided to implement Sakoku (1633-1868), which wouldn't exactly help your proposal.
To get Japan to maneuver its way into being a world power by interfering in China, you'll have to somehow prevent China from ever becoming "China" in the first place. Maybe with a POD as far back as preventing Qin Shihuang, the duchies of China could all have developed into their own nations, with competing interests that Japan could have played off of. But the butterflies from that will alter the course of the development of Japanese civilization itself, since OTL Japan relied on a heavy dosage of Chinese cultural imports to develop the way it did. Would the Japan in TTL even still be recognizably Japan as we know it?
This situation would lead to an immense amount of butterflies to the point where China, Korea, and/or Japan probably wouldn't even exist. For example, assuming that China somehow continues to remain divided, the lack of a Qin analogue ITTL could lead to a much more influential Gojoseon, which could lead it to eventually pressure the corresponding state(s) in the southern peninsula and seek to extend its influence among the various Japanese statelets, resulting in much more significant transmissions of Chinese and Korean culture to the archipelago centuries earlier. Considering that Gojoseon had already been relatively centralized around 700-300 BC, based on archeological evidence, it's theoretically possible that Korea could wield much more political influence over Japan than it did IOTL, which is the opposite of the OP's general intent.