Okay, so I know a lot about the ideological differences between the two countries that grew ever since 1953 (I also label Mao's general dislike of Khrushchev's foreign policy as an 'ideological' issue).
But the purely ideological reasoning seem to be lackluster. Surely, the leaders of the two most powerful communist nations in the world at that moment should have been mostly guided by objective reasons unrelated to petty ideological struggle. Especially since their alliance should have been quite powerful (Soviet industrial base combined with Chinese population numbers?), but, for some reason, politicians of the two countries chose rivalry as opposed to increased cooperation.
Why?
There was never much trust between the Soviets and the Chinese Communists even before the Chinese communist victory in the Chinese civil war. In the course of the Chinese Civil War between the Kuomintang (Chinese Nationalists, or KMT/GMD) and the CPC (Communist Party of China) for most of the war the Kuomintang was by far the dominant controller of China, while the CPC was essentially relegated to a small area. As such, while ideologically the Soviet Union may have been closer to the CPC, they also wanted to cultivate a good relationship with the de jure rulers of China, who also had socialist-lite policies. Soviet advisers were sent to help the KMT with their modernization activities, and also Soviet aircraft were sent to help fight the Japanese when the Japanese invaded China in the late 1930s, in the course of the Second Sino-Japanese War. One key incident was the Xi'an incident, where a rogue warlord abducted the leader of the KMT, Chiang Kai Shek, in an effort to force a peace between the KMT and the CPC against the Japanese threat. The CPC allegedly wanted to have Chiang killed, but the Soviet Union intervened, under the grounds that Chiang was the only one keeping China more or less united against the Japanese. This sort of foreign intervention by the Soviet Union against the Chinese communists earned their ire, such that while they may have been ideological allies (and the Soviet Union provided aid to the Communists that became important to their victory) the CPC did not trust the USSR, and while they may have been an ideological ally, they also were a geopolitical rival.