I believe Chiang had announced Chen Cheng as his successor should he die during the war. That authority is on paper. In actuality, we know Chiang - particular at this time - ruled less by institutional authority, then by his status as paramount leader and his political skill at managing various subordinates of dubious loyalty.
Chen Cheng would need to deal with internal rivals within the core KMT - like He Yingqin, the members of the Soong dynasty, and warlord factions like the New Guangxi Clique of Li Zongren and Bai Chongxi, Long Yun ruler of Yunnan, and others. I believe he did have an ally with T.V. Soong though, Chiang's brother-in-law who was one of the financial leaders of the KMT.
I don't see any replacement leader doing a better job than Chiang Kai-Shek. No one has the political authority to hold everyone together, and thus will have less real authority than Chiang.
However, Chen Cheng was by all accounts a very capable man, and he did a good job running Taiwan for Chiang. He could probably keep China in the war until the end. Big question mark is how well he relates to American advisors sent over. ITOL, there was evidence that Stilwell got along decently with Chen Cheng and TV Soong, so it is possible that this relationship might be greatly improved. Whether this has any inpact during the war is doubtful as long as the Burma Road is closed, but it might leave the KMT with a more postive image in the US, and might leave the Nationalist Army in a better status.
Whether he'd do any better after the war handling the postwar struggle against the Communists, is a more difficult question. Chen made major mistakes in Manchuria that helped the Communists, but he ruled Taiwan well. If Chen is less confident of military victory than Chiang was, and concentrated on important reforms, we might have a situation where the north is ruled by the Communists, bu the KMT can hold onto the south. Of course, it may lead to the same result as OTL.