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.