How does Egypt compare to ancient Egypt?
The simple answer is that it doesn't. However, modern Britain has little in common with ancient Britain either. Of course, both countries claim their respective lands' treasures such as the Sphinx (Egypt) or Stonehenge (Britain). If we contrast Britain with Egypt, the ancient word for a bird trap in Egypt, or skeet, is also the word used in England to describe a clay pigeon shooting range. The English word "south" is the same in ancient Egyptian - sut or sud. Such things are perhaps rare but they do show that ancient Egypt had connections with ancient Britain as the modern nations do. In fact, a century ago, Britain ruled or administered Egypt.
So the answer is not so simple. It might therefore be easier to look at some aspects of modern Egypt that ancient Egypt did not have.
Perhaps the most obvious contrast to compare is the religion of ancient and modern Egypt. Today, Islam, and to a lesser extent some Christianity, is the religion of Egypt. But Islam has only been significant in Egypt for 1400 years since Mohammad. Some Muslims will say that "Islam" means "righteous" so that many Egyptians well before Mohammad were also "righteous" and therefore Islamic. Does that mean the people who worshipped the many gods of ancient Egypt were "righteous"? In ancient Egypt, the sun god Ra was popular but across the Red Sea in Arabia, the moon was a god. That is because the Arabs lived their working lives at night to avoid the heat of the day so they worshipped the moon. But in Egypt, with its mighty river and cool shading trees, the sun was far less harsh and dramatic and much more popular as an object of reverence. Today, the moon is the main symbol on the flags of Muslim countries (but not Egypt's).
Egypt today probably has a much larger proportion of people who are not religious at all as their somewhat neutral flag suggests. The popular uprisings in Egypt stem from the problems of competing philosophical and religious ideas. This is something ancient and modern Egypt probably share.
One of the great philosophical questions facing the Egyptians of 586 BC was the total routing, sacking, razing and near-total depopulation of ancient Israel by Nebuchadnezzar the Chaldean-Babylonian. Many people at the time believed the Seed of the Woman Programme, first announced in the Bible when Adam and Eve received God's prophecy of the outcome of their disobedience in the Garden of Eden, had been abandoned after Israel's demise in 586 BC. The Egyptian king at the time, Merneptah Baenre Meriamun Hotephirmaat, or Pharaoh Hophra of Jeremiah 44:30 in the Bible, recorded on a stone stele, "Israel's Seed is destroyed (or castrated); the Land razed (or shaved) to the ground". After Jesus of Nazareth was born (7-6 BC), many Egyptians repented and believed again in the Promise of the Seed after Jesus' resurrection (30 AD). Thus much of Egypt became Christian between 30-650 AD. Then the Muslims conquered Egypt resulting in many Egyptians turning to Islam because of the corruption in the state church systems of the time. Mohammad's reforms were often preferred over his revised theology. A parallel thing happened after Luther in Europe (1600 AD). But problems do not just exist in religions. The academics in the universities believe Merneptah ruled Egypt in 1210 BC when he was supposed to have written the "Israel" or "Merneptah Stele". This contributor understands the Merneptah Stele is now on prominent display in the Cairo Museum in a similar fashion to the Rosetta Stone in the British Museum near the main entrance (although we stand to be corrected regarding the Cairo museum).
However, that is perhaps the most interesting comparison between ancient and modern Egypt - their policy and attitude towards Israel their neighbour across (as Australians and New Zealanders say) "the ditch" (Reed Sea, Red Sea, Suez Canal). Israel and Egypt, such close neighbours, their histories so closely entwined, according to the Bible. Yet modern historians say the "Merneptah Stele" is the "only" or "first" reference in ancient Egyptian literature to the Jewish nation whose history is so carefully outlined in the Bible. In modern Egypt, Israel is in the news lots of times. Apparently, according to Egyptologists and historians, the opposite was the case. And there lies a big tale. By not knowing what Egypt's history really was, as that conundrum must surely attest, it is almost impossible to answer this question. But it is an important question and if the answer were properly and thoroughly canvassed we might actually learn something. Probably, many people will be rather shocked to say the least.
*but not Egypt's