Rome and Athens are the two great capitals of classical antiquity, and travelers choosing between them are really choosing between two different empires and two different paces of city.
Rome has the edge in sheer density and preservation — the Colosseum, Roman Forum, and Pantheon are astonishingly intact and layered throughout a living, modern city. Athens' Parthenon and Ancient Agora are older and arguably more historically foundational — the birthplace of democracy — but the ruins themselves are more fragmentary, concentrated mainly around the Acropolis.
Rome's Vatican Museums & Sistine Chapel is one of the greatest art collections on earth, spanning far beyond antiquity into the Renaissance. Athens' Acropolis Museum and National Archaeological Museum are excellent but narrower in scope, focused specifically on Greek antiquity.
Rome's Trastevere and Athens' Plaka both offer atmospheric old-town dining, but Athens is noticeably cheaper and more laid-back, with a slower, more Mediterranean rhythm. Rome is busier, grander, and geared more toward a fast-paced sightseeing trip.
Athens has a strong edge here: Delphi and Cape Sounion & Temple of Poseidon are both dramatic, easy day trips, and the Greek islands are a realistic extension for travelers with extra time. Rome's best day trip, Pompeii & Mount Vesuvius, is excellent but requires more travel time and is really a full-day commitment.
Choose Rome for the density and preservation of its ruins, plus the Vatican's unmatched art collection. Choose Athens for a more affordable, laid-back pace, strong day trips, and easy access to the Greek islands. They're not connected by a quick train — flying between them takes under two hours, making a combined trip realistic for a longer Mediterranean itinerary.