There are many things similar and different between ancient China, Egypt and the Sumerians were lead by the high priests. One important thing is how the three kingdoms were ruled. With Egypt they had Pharaohs, which were appointed by their gods. In Sumeria they had. With Chinese leaders were mostly conquers which lead for a while and passed down through their families. Also each one of the civilizations had made their first writing systems but the writing was different with Chinese but somewhat the same with Egypt and Sumeria.
In the Old kingdom Egypt and Sumeria the words were mostly symbols or pictures. With Chinese there are plenty of lines in different directions, which mostly are like symbols, which is almost like the new kingdom Egypt. With China outside wars were not a worry due to the fact of the mountains and the sea and the Great Wall of China. But with Egypt and Sumeria there were plenty of rivers to get to each city which were a good source for conquers to try and get the land. Also with Egypt and Sumeria there were rivers, which gave them good soil, and a good resource for water and transportation for trades.
In China they didn't really have a chance to trade with other countries but it was big enough to trade with themselves and to fight themselves for other Lords to get more land then what they already had. All three civilizations had temples to hold their gods, priests or Pharaohs. These were for the afterlife for their leaders to live good in the afterlife. They all put precious things in there with their leaders.
This was for them to live well in the afterlife. Each of the civilizations have their own religions. Each civilization had their own believes in the gods that ruled over them or if it is their Pharaohs or leaders that will watch over them. These are some things of how each ancient civilization was the same or different in some ways. They all had a lot in common and really barely knew of each other and what others did in the other places.