For those living in the actual period of transition, let's say between 31 BCE and 14 CE (the reign of Octavian-Augustus), the most immediate change was a relatively calm, peaceful era of prosperity. This is often called the pax Augusta, the "Augustan Peace. Rome had endured a nearly-constant barrage of civic violence and civil war since the late 2nd century, nearly a hundred years of intermittent turmoil and strife. The Gracchi Brothers riots, Marius, the Social War, Cinna, Sulla, the proscriptions, the tumultuous 60s, the first triumvirate, Caesar's crazy consulship, Clodius and Milo, the Civil War, the second triumvirate, the second Civil War, ultimately culminating at the Battle of Actium. When Octavian finally took sole power and made sure there would be no more rivals to his claim, there was lasting peace. There was nobody alive by then who remembered anything except violence.

It was a time of economic boom. Roman agricultural, mining, and manufacturing power expanded sharply in this general period, thanks in part to a massive redistribution of population: the settlement of over 100,000 thousand soldiers in veteran colonies all across the Mediterranean. Many had been under arms for years, decades, and their settlement in new, far-flung towns contributed to the deposition of a massive amount of capital in those regions. These soldiers had money in their pockets, thanks to years of war and years of (essentially) bribing by the triumvirs, and they proved ready to spend it. This spurred on urbanization and agricultural exploitation on an organized and massive scale, especially in the west in provinces like North Africa, Hispania, and Gaul. Carthage, and all the hinterland of Tunisia, got a massive resettlement and reorganization under Augustus, and quickly became one of the richest and most productive regions in the Empire. It was a similar story at Antioch, or at Merida in Spain, or at Nimes or Arles in Gaul.

For the ordinary citizens of the Capital, it was a time of stability. The city ran smoothly during this period, for the most part, and the fruits of prosperity were pouring in. I'm not an ancient economist and I do not know how exactly the plebs benefitted in their day-to-day as far as availability of goods, or prices, but at the very least we know that Octavian's, um, acquisition of Egypt meant that grain ships were arriving at Ostia on the regular, laden with free food for the common folk.

The experience of the ordinary Roman denizen as s/he moved about the city was completely changed under Augustus. In the res gestae he brags that he found Rome a city of brick and left her a city of marble, and there is a lot of truth to that. The edifices of the city were transformed in this period, with major building or restoration projects all over the place. Caesar's forum addition was finished and embellished, and Augustus' own addition was completed, with the magnificent temple of Mars Ultor and its statue-laden wings. The Altar of Peace and the great horologium were installed in the Campus Martius. Under Augustus, the Palatine Hill began its conversion from exclusive elite neighborhood to Imperial Palace. The city had always been a locus of monumentality, but under Augustus things really start to become Monumental with a capital "M," and this trend would only continue under future emperors. Under the Empire, the city slowly but surely transformed into a massive announcement of Roman military, cultural, and engineering might. Augustus set the tone of how, where, and why an emperor should build things in cities, especially the City.

In other spheres, not much changed at all. Religious festivals came and went exactly as they had under the Republic. The holiday cycle remained much the same, with a few Imperial additions here and there. There was a new Cult to the Deified Julius Caesar, and to him would be added further emperors, but Rome with filled with cults and there was always room for more. There was a trend towards density in the Capital, with about a million inhabitants by 1 CE, but this trend had already been happening in the first century BCE and was part of a general urbanization movement in the Late Republic. Those who complained about crowding in 10 BCE had probably also been complaining about it in 40 BCE.