How could
Chen Youliang and his faction of Red Turbans could not only defeat Zhu Yuanzhang, but as well re-establish his dynasty as ruling all over China after defeating Yuans?
What would that mean for a Dahan China? Would that mean a lesser focus on Budhism and re-establishment of pre-Mongols traditions?
Or would the more cunning, maybe brutal, nature of Chen Youliang would have different priorities?
The Battle of Poyang Lake in 1363 was the decisive confrontation between Ming and Han, and it absolutely could have gone either way. After that, Chen can follow more or less the same blueprint that Zhu Yuanzhang did IRL in terms of consolidating his strength in the south and ultimately finishing off the remnants of the Yuan. If you want an earlier POD, Zhu lured Chen into a trap at Longwan in 1360, seizing the initiative in the war between Ming and Han and capturing lots of Chen’s ships.
The question of how a dynasty led by Chen would differ from Zhu’s Ming Dynasty is trickier. Both guys had abandoned the millennarian White Lotus Buddhism that characterized the early Red Turbans, so I don’t think you’d see any religious shenanigans from Chen. I’m honestly not sure what the major short-term differences would be. You note the “cunning, brutal nature of Chen Youliang,” and sure, he was both - but so was Zhu Yuanzhang. Maybe the biggest difference would come after Chen was dead. I doubt that any of his offspring could match the grandiose megalomania of the Yongle Emperor in real life.
Also, I have to note that the most interesting character in this period is neither Zhu nor Chen. It’s Ming Yuzhen, the Manichean warlord of Sichuan! I wrote a brief and abortive TL about him
here, if you’ll forgive the shameless self-promotion.