The major difference between New Kingdom Egypt and the older systems was that the New Kingdom was more modernized and professionalized and was also more aggressive in its foreign policy.
In the New Kingdom, the military became a much more professional organization. This was in contrast to the old system in which regional governors would get up what men they could and come to fight for the Pharaoh when needed. As the military became more professionalized, it also became more powerful in political terms. In the New Kingdom, viziers (the most important bureaucrats, people who actually ran the kingdom) came only from the military.
With this more powerful military (and the new weapons and tactics the Egyptians had learned from the Hyksos), Egypt became more aggressive in its foreign policy. It was at this point that Egypt conquered Nubia and occupied and controlled areas of Palestine and Phoenicia.
In these ways, the New Kingdom was more organized and modern than the older kingdoms. This allowed Egypt to become more of a regional power with something of an empire.
It is possible to divide ancient Egyptian history into three time periods. They are the Old Kingdom, the Middle Kingdom, and the New Kingdom.
The Old Kingdom existed from 2700 BCE-2200 BCE. The Pharaohs were completely in charge. They built many pyramids that were paid for with money from the treasury. The Pharaohs were considered to be G-d’s representative on Earth. The capital of the Old Kingdom was at Memphis. The Upper Nile and the Lower Nile met at Memphis.
The Middle Kingdom lasted from 2100 BCE-1800 BCE. During this time, trade was very prosperous. The Egyptians strengthened their military. There was a growth in the arts, science, and literature. Pharaohs were no longer buried in pyramids. Instead, they were buried in hidden tombs. The capital was at Thebes.
The New Kingdom lasted from 1500 BCE to 1000 BCE. New items were introduced during this time. These included the horse, chariots, and bronze weapons. The Kings were buried in the Valley of the Kings. The Egyptians moved beyond their borders. For example, they went to Nubia and modern day Israel. This period of time is considered a very prosperous time period. Egypt also reached the height of its power during this time.