^I'm ^not ^sure ^what ^you ^mean ^by ^"examining ^Rome". ^If ^you ^mean ^something ^like ^walking ^through ^the ^city ^of ^Rome, ^this ^would ^be ^my ^answer:

 

Rome has changed massively between the reign of Augustus (27 BCE - 14) and that of Constantine (306-337). Most major monuments are completely new to you. A short list of prominent examples:

 

First century

• The Colosseum would stand where houses stood during your time, it was built by the Flavian emperors (69-96)
• Several new forums would have been added near the Forum Romanum and the already familiar forums of Caesar and Augustus
• The Arch of Titus, celebrating Rome's victory in the Jewish Revolt

Second century

• The Pantheon would not be the one you know, built by Agrippa, but a completely different (and more impressive) building built by Hadrian. Surprisingly the original inscription remains
• Trajan's Market
• The Column of Trajan depicting victories in Dacia, an area that didn't yet belong to the Roman Empire in your time
• The Column of Marcus Aurelius
• The Temple of Faustina and Antoninus Pius on the Forum Romanum

Third century

• The Aurelian Wall, a new city wall
• The enormous Baths of Diocletian
• The likewise enormous Baths of Caracalla

Fourth century (up until the end of Constantine's reign)

• The Old St. Peter's Basilica would be under construction, a church being built by emperor Constantine for a religion you've never heard of
• The Arch of Constantine, celebrating a victory in the civil war against Maxentius
• The Basilica of Constantine and Maxentius on the Forum Romanum

Some other differences

• The coins have largely different names from the ones you knew, they're also heavily debased compared to the Augustan age
• People from all over the empire are citizens now due to the Edict of Caracalla in 212

Some similarities

It may surprise you to learn that some things would be very much recognizable to you. For example:

• The number of people in Rome would be roughly the same, although Augustus' age was before the population reached a peak while Constantine reigns after it reached its peak.
• The Circus Maximus has been improved upon, but has kept most of its original design
• The Curia Julia, where the Senate debates on the Forum Romanum is pretty much the same building you know
• The Theatre of Pompey
• Emperors are still calling themselves "Caesar" and "Augustus", even though no-one of the Julio-Claudian family remains
• The city of Ostia is probably still Rome's dominant harbour, although it is in heavy competition with Portus (which is entirely unfamiliar to you)

Ok, first things first I am promoting you to Senator, because the Equestrian Order is a rather difficult group to define. In many ways it is essentially a tax bracket rather than a socio-political organization as such, and most of the stuff we have is about Senators and the associated social circles anyway, and I think that is what you are looking for. So congratulations!

Perhaps the first thing you notice as you step into the Curia is that there is a much more diverse bunch inhabiting it. The ruling class of Augustus was by no means homogeneous, and one of his great policies was in using local elites rather than running roughshod over them, but he was at the beginning of a process and you are at the end. The current emperor is from Moesia, basically the modern Balkans, and he grew up in Britain. When you disappeared mysteriously Moesia was a semi-Roman region of barbarians and bandits, and Britain wasn't even Roman. In a very immediate way, the accent Constantine and his inner circle speaks with did not exist in your time, but even outside of that the Senate is thronged with Greeks, North Africans, Spanish, Gauls and Syrians--although still favoring the Latin West. On the other hand, these people would be much more similar to each other than an equivalent group would have been in Augustan time, because again, that is at the beginning of a process you are seeing the end of.

For government service, you will see immediately that things are more bureaucratized. The early Empire was essentially run through overlapping personal connections and the main job of, say, a provincial governor was to ensure that the conflict resulting from this would not erupt in violence, or at least would be pushed towards productive ends. The government now is much more concerned about centralization, and from that a new class of elite has arisen. In the Augustan period one could say that the Empire was run by traditional elites transformed by an Imperial culture, but now the highest officials are truly political and truly imperial. They are, in a sense, mandarins or literatti rather than nobiles.

For religion, to an extent the emperor and his inner circle follow a teaching that did not exist for you, but more importantly the nature of imperial religions had changed. In the Augustan period, worship was still dominated by local practices, but now those have been transformed by a large series of massive, Imperial wide cults. Neither Christ, nor Mithras, nor Sol Invictus existed in a substantial was in the Augustan period, but they are now a crucial part of imperial culture.

These are just three things, but I hope it gives you an idea of how society became more "imperial." Greg Woolf is certainly the scholar to see for this, and I have heard his new Rome: An Empire's Story is intended for a more non-academic audience.

If I could ask a follow up, what would have been different for the entire Empire, rather than just for the city of Rome?