How can we prove that Egyptian engineering was superior to any other of the time?

Answer 1

We can't. The pyramids were of course amazing structures, but so were the temples and monuments of Assyria and Babylon. Being able to (at least in some pyramids) aim a light shaft from the inner chambers to an exact point in the sky was of course very clever, but not a feat of engineering that was of any use to anybody, except for the spirit of the dead Pharaoh - hopefully.
The Egyptians had some knowledge of irrigation engineering, but that was certainly not superior to the contemporary engineering in that field of Mesopotamia. They developed some skills at boat-building, but none that made those boats fit for the open seas. That was something the Phoenicians developed. It was Mesopotamia that came up with the most important invention of all, the wheel. One problem with Egyptian engineering was that once they had invented a technique, they rarely developed it anymore.
Finally, that Egyptian lack of innovation caused their engineering techniques to be superseded in the era of the Ptolemaic Pharaohs by Greek and Roman engineering.