Oogway represents Daoism with its search for inner peace and going with the flow/dao. Shifu, on the other hand, represents Confucianism with its concerns for moral duty and worldly social harmony. The internal and external, immaterial and material—each has a role in the construction of a philosophy conducive to success.
"Oogway explains that he can not make the peach tree blossom or bear fruit before it is ready. Shifu retorts that there are things that can be controlled like when the fruit falls or where the seeds are planted. Oogway finalizes by saying that no matter what is done, the tree will still grow to be a peach tree, instead of any other kind of tree and that great things can happen if it is helped and nurtured. Oogway argues the point of Daoism and that nature will take its course. Shifu argues the point of Confucianism and that everything has order." [1]
Also shameless plug for my essay about Culture, Philosophy, and Reinforcement Learning which comments on similar dualities and their relations. [2]
[1] https://medium.com/@gvreligion/quit-dont-quit-noodles-don-t-...
[2] https://medium.com/@rohan.pandey/culture-philosophy-and-rein...