Cats did probably hunt mice in the ancient world. There are examples of ancient Egyptian art that show cat and mouse opposed, facing each other, indicating this relationship. Evidence of cats are also noted particularly in and around ancient granaries.

Cat burials are found in and around ancient Egypt indicating they were to some extent treated/loved by people similar to our relationship with pets today.

In terms of more nuanced feline behavior, I don’t have any ancient examples coming to mind, but I am reminded of an 18th century Japanese text, Gazu Hyakki Yagyo. This book includes a tale of a cat that is able to open a drawer, steal a handkerchief, and proceeds to plays with the handkerchief with some other cats. When the cat’s theft is observed by one of its human owners it immediately runs away. This seems to be consistent with contemporary experience.

While changes in cats behavior over the course of their domestication is to be expected, I think these will be harder for us to ascertain than the similarities, as their behavior is regularly characterized through religious and social lenses that evolve faster than their actual behavior would. The only thing coming to mind would be advanced studies of the changes in nutrition and morphology which I’m not really aware of. For example, we know that ancient cats were bigger than average size today, was there a related behavioral change?

Interesting question.

The Cats in Ancient Egypt - Jaromir Malek Early Taming of the Cat in Cyprus - vigne, gullaine, debue, haye, gerard Gazu Hyakki Yagyo - Toriyama Sekien