Inspired by the late Christopher Hitchens - in a debate a theist brings up the fact that many churches are beautiful works citing the Sistine Chapel. Hitch counters by saying that the Parthenon is his favourite structure but that doesn’t mean he believes in the cult of Palace Athena.
So, ridiculous hypothetical time - two fairly small meteorites are heading towards Earth. One heading straight towards the the Parthenon in Athens, the other the Sistine Chapel in Rome. If they hit they will cause total loss of the building it hits and significant damage to the surrounding area (The Acropolis of Athens in the former case, the Apostolic Palace and Il Vaticano in the latter case). Both areas have been completely evacuated so there will be zero casualties in either case. You can use a one-shot laser to destroy one of the approaching space menaces. Which do you chose?
I don’t know enough about those buildings to say one way or the other. But the SC is a present residence and hopefully the Pope is paid up on his homeowners insurance, and sort of his responsibility. The Parathion is already in ruins and can it get much worse. Athena has long since abandoned the building and it is just a shell in monument to her.
Either will be a loss only to the people who care about them. I expect both are of marginal importance to most of humanity. Save neither or flip a coin. Makes no difference to me whatever the outcome.
I voted for the Parthenon as it represents a link to our ancient past. The Sistine Chapel, while beautiful and a significant piece of work, is one of many from that time period and represents a tradition that still is active today. I can see an argument either way.
I personally care more about the Parthenon, but am inclined to say that saving the Sistine Chapel would be better from an art history perspective. The Parthenon is already a ruin (it only looks as good as it does because of modern reconstruction work) and because most of the sculptures from the Parthenon have long since been removed and are housed in various museums. So even the total destruction of the Parthenon site would not result in the destruction of much of the historically and culturally significant artwork that once resided there.
However, the destruction of the Parthenon might have a much more serious effect on the local economy than would the destruction of the Sistine Chapel. Greece probably needs all the tourism dollars it can get right now, and isn’t in much of a position to fund a reconstruction of the Parthenon on the original site. I imagine the Catholic church could raise enough money from its adherents to start building a new church and papal palace soon. There are plenty of other culturally significant things to see in Rome and many people would visit the new church for religious reasons even if it wasn’t very attractive, so I don’t know that tourism would be affected that badly.
In fairness to the Parthenon, it’s amazing that it’s survived this long relatively intact, through myriad empires. It also survived getting blown up (!) in the 17th century. The Turks used it to store gunpowder. Venetians fired cannons at it. What a sad moment that was.