How did the Burmese and Vietnamese people resist subjection?

They responded in both similar and different ways. Both resisted colonial settlement and rule, sometimes violently, always persistently. The Buddhists resisted in both nations, but were more important in the Burmese resistance to colonialism by the British. The Brits also owned India at the time, and made Burma a province of that colony, so they had to deal with being subcolonized by India too.