So, one common thing that's very observable is how much more Hellenized Latin becomes.

We have the 'golden age' of Latin literature and here the examples are Cicero, Vergil, Caesar, Catullus, Horace, and Titus Livius.

When we look at somebody like Seneca, for example, we still see a strong Latin presence but one that is much more 'hellenized' and Seneca indeed was an enormous admirer of the Attic writers.

Way into the Antonine and Severan era, the Latin language is very much a sort of quasi-Greek language. Examples of such Latin literature with heavy Greek borrowing is the Attic Nights by Gellius.

Finally, we see way into the later centuries writers like Lactantius and Firmicus Maternus who write in a Latin that is not only very Hellenized in neologisms but in style and tone as well, sometimes even borrowing directly from Plato, Aristotle, Homer, Xenophon, among others.

Now, what's not often talked about is how this changed the customs and manners of Rome, the overall culture. How names change, how rhetoric changes, together with just regular way of thinking.

One philhellene that people often miss is old Marcus Tullius Cicero who explodes in popularity in the late empire. You can see how many of the later Latin writers like Jerome, Augustine, Paulinus, Orosius, etc... all very much have a sort of 'Ciceronian' philosophy, but with a Christian sense. That's to say they cherry-pick what they like about Cicero and use it in their own day.

Cicero, of course, we know essentially bridged the Greek philosophic tradition, the Hellenistic schools of thought, into the Roman world. His works like Officis, De Republica, Finibus Bonum et Malum, De Divinatione, etc ... are really only understandable if you can grasp all the references he makes to the Greeks.