Both Phan Boi Chau and Phan Chu Trinh were nationalists. Both of them wanted to free Vietnam from colonial occupation.
Difference:
(i) Phan Boi Chau: He was a Confucian scholar. He formed a revolutionary society in 1903, with Prince Cuong as the head. He wrote a book, The History of the Loss of Vietnam, which became bestseller in Vietnam and China. He focussed on two topics in this book:
(a) the loss of sovereignty, and
(b) the severing of ties with China—ties that bound the elites of two countries within a shared culture.
(ii) Phan Chu Trinh: He did not favour monarchy and opposed the idea of resisting the French with the help of court. He wanted to establish a democratic republic. He was profoundly influenced by the west and did not want total rejection of western civilisation. He demanded that the French set up legal and educational institutions and developed agriculture and industries.