There are three ways in which the age of Pericles and the Pax Romana of Augustus were similar.

1. Both ages experienced a renaissance in literature and arts. On the Greek side, Pericles and his regime viewed themselves as a school for the other Greek states. And on the Roman side, the Augustan age produced notable authors such as Vergil and Horace.

2. Both ages were an age of great building. For example Pericles did extensive work on the Acropolis and Augustus in the Res Gestae states that restored or built no less than 82 temples.

3. Both ages were a time of expansion. The Athenians took over the Delian league and Octavian (Augustus) defeated Antony and Celopatra at Actium in 31 BC.

As for longevity, The Augustan age or the Pax Romana lasted much longer. Pericles' world was cut short by the Peloponnesian War.

It seems to me that these two eras are pretty similar.  They are both characterized by relatively long periods of peace both within the society and in the relations with foreign countries.

Also in both cases, the societies benefitted from the peace that the periods gave them.  Because of this peace, they were able to devote their energies and resources to such things as art, literature, philosophy and other such things.  This meant that both societies enjoyed something of a Golden Age.

So these two periods are really quite similar -- times of peace allowed the societies to flower culturally.

How is the Pax Romana similar to the Age of Pericles?

This is a great question. Pax Romana is like the Age of Pericles in a few ways. Let me first give you the historical context. The late Republic was a time of turmoil and violence. There were even two civil wars. Sulla fought Marius, and Caesar fought Pompey the Great. These two wars were extremely costly, to say the least. Within this context, everything seemed to come apart. Within this context, Augustus steps in and brings peace.

He is like Pericles because one great leader brings prosperity. During this time, we see some of the best poetry in Latin and great building projects. Augustus says in the Res Gestae (the accomplishment of his life) that he left Rome as a city of marble. To be sure he is exaggerating, but the point remains that there were some great developments. Pericles did the same thing. He was a patron of the arts and started work on the acropolis. In short, both ages experienced a renaissance.