The Chinese mandate of Heaven was established by the Zhou dynasty as a description of how an emperor could rule or be deposed. It said that as long as the emperor behaved well, then he would be in favor of God and his rule would continue. However, if another clan should receive word the gods that they were displeased with the current dynasty, then you had the right to be overthrown. These signals, (that an dynasty was not being 'good') could be shown through nature with floods, hurricanes, famine, etc. The European divine right of kings said that a king was essentially a 'messenger from God' and that his supreme authority was to be obeyed at all costs.
It meant that to question the king's authority was to question God. The difference btw the Chinese mandate and the DRO kings is that no one is given authority to overthrown the EU kings. If God wanted them removed, then a natural act would happen, and the king would die. Other than that, you were supposed to obey his authority whether you agreed with it or not. Secondly, in the Chinese one you are supposed to be good or your throne could be taken away.
This made you follow strict rituals that were in place by you ancestors. The EU version, the king could be evil and mean, and no one could challenge him. He didn't have to be nice or good if he didn't' want to. He could do whatever he wants.
The similarity is that both are reliant on God giving them their authority. The ppl see both as being in place b / c heaven commanded it. Therefore, both theories give both rulers and emperors abs. control over their subjects by making them associate them with essentially heaven's "ambassadors.".