Both were fought over the government and gave more power to the common man.
False this is not correct
Tim Keller on Dr. King’s rejection of relativism:
When Martin Luther King Jr. confronted racism in the white church in the South, he did not call on Southern churches to become more secular. Read his sermons and “Letter from the Birmingham Jail” and see how he argued. He invoked God’s moral law and the Scripture. He called white Christians to be more true to their own beliefs and to realize what the Bible really teaches. He did not say, “Truth is relative and everyone is free to determine what is right or wrong for them.” If everything is relative, there would have been no incentive for white people in the south to give up their power. Rather, Dr. King invoked the prophet Amos, who said, “Let justice roll down like waters, and righteousness as a mighty stream.” The greatest champion of justice in our era knew the antidote to racism was not less Christianity, but a deeper and truer Christianity.
(Reason for God, pp.64-65)
The American colonists were justified in doing this simply because their colonies had become too big and too important to be treated as a colony by the British. The British should have given the colonies some autonomy, but they did not. The analogy I like to use is that of teens and their parents. Parents have to give teens more independence as they grow up. If they do not, the teens may justifiably rebel.
The British were not, on the whole, brutal or oppressive towards the colonists. However, they would not let the colonists have much in the way of self-rule. This had been fine when the colonies were still small and economically weak. By the 1760s and 1770s, however, the colonies were "teenagers." They were big and strong enough to expect some autonomy. When Britain reacted to requests for autonomy by being more strict, the colonists were justified in rebelling.