(This answer will be mainly focused on antiquity in the Near East and Central Asia, which is primarily what I study. It might apply to ancient civilizations in other parts of the world, too... or not.)

In the bronze age, it wasn't individual people who had distinct personalities, aesthetics and lifestyles -- whole civilizations did.

As recently as the early Middle Ages, when most of Europe and West Asia was going monotheistic, life in an Arabian city would've included not only a different language from anywhere in Europe, but also distinctly different styles of music, art and architecture; different ways of making and interpreting laws; different approaches to education, and women's rights, and innumerable other aspects of society.

But even by the 800s or so, many aspects of civilization were converging toward universal mediums. European and Arabic scholars alike were studying Plato and Aristotle (whose works were introduced to the East by the peoples who accompanied Alexander the Great's army), were observing laws based on ancient Judaic traditions, and trading and exchanging ideas within a world linked up by the Roman and Persian Empires. By late antiquity, no self-respecting Eurasian empire could afford to be "out of the loop."

Now, go back 1,900 years before that. The Egyptian Middle Kingdom, the Hittites in Mesopotamia, and the Minoans in the Mediterranean... all linked into a vast trading web, exchanging goods and ideas from Scandinavia all the way to Iran -- but none of these civilizations have common history; no single ancient empire that brought them all together in the distant past. They evolved semi-independently, discovering one another over the centuries, establishing and cultivating those relationships for the first time in world history. And meanwhile, they continued to develop their own "personalities" -- the languages, gods, clothing styles, music, architecture, art and warfare that set them apart -- influenced by nearby civilizations, sure. But sprouting from completely different cultural substrates.

Now go back 1,500 years before that. Egypt is at the height of its Old Kingdom. Sumer rules Mesopotamia. Further east, you've got the Elamites in Iran, the Bactria-Margiana Archaeological Complex (BMAC) in Turkmenistan, and Harappa and Mohenjo Daro in the Indus Valley. Some of them seem to have traded with each other -- in fact, we're just recently beginning to realize how interconnected the regional economies of the early bronze age may actually have been -- but this far back, every one of them is easily distinguishable from all the others, on every level: art, architecture, government, economy, military, religion... each one of these civilizations is like a whole separate world to explore.

And that, I think, is one of the main reasons ancient civilizations are so fascinating. Ask what life is like in 21st-century Istanbul or Baghdad, for example, and although there'll be a lot of surface differences from life in Germany or China, most of the phones, cars, clothing brands, furniture, TV shows, functional architectural styles, etc. won't really be strikingly different from most other places on earth.

The further back in time you go, the more those similarities vanish, and you're left with a lifetime of questions about every new civilization you discover.