Roman Egypt and Ancient Egypt were separated by a large period called Ptolematic Egypt (or Greek Egypt). During this time Alexander the Great rolled in and took over everything! His Greek lifestyle and culture was introduced to Egypt so that by the time the Romans showed up to take over around 36 BCE, everything was pretty hybridized.

Alexandria was a city built by the Greeks and during the Roman period the laws you followed were compeltely dependant on what citizenship you held. If you were native Egyptian, Greek, Roman, or even Jewish, you had your own set of laws! Confusing to say the least. Greek was the language of the land during Ptolemaic Egypt and stayed around during Roman Egypt (which matched the rest of the Eastern Empire).

In Roman Egypt everything came down to where you lived and what kind of citizenship you held, and everything existed in this weird in-between culture. The government of all Roman Egypt was Roman and run in Latin, but the provincial and town government was really more Greek and run in Greek, but the native population still spoke and wrote in Egyptian as did most merchants. The religion was also mixed, with traditional Egyptian gods like Horus mixed in with Greek/Roman ones like Zeus/Jupiter, and even some hybrid ones like Serapis.

tl;dr - It was pretty similar in a lot of ways, but everything came down to where your family was from.