Italy was hit by a series of earthquakes in 2016, including a 6.6. Certainly there was a lot of damage, including in Rome, but most stone structures survived.
Damage from Earthquakes is usually localised - how close you are to the fault really really matters (until you get up to the mega-quakes that can affect much of a small country).
Christchurch was hit by a 6.2, but most of the damage occurred on the suburban south-Eastern half of the city, and the commercial buildings in the city centre which were more vulnerable. 10’s of kilometres away and no significant damage to buildings.
The magnitude 7.8 Kaikoura earthquake in 2016 had an epicentre 100km away from Christchurch, and there was no damage here in Christchurch.
Several of the earthquakes Italy has experienced were reasonably close to Rome. None have had the epicenter there to my knowledge, though.
It’s perhaps more interesting to ask what non-stone buildings have survived 1000 years. I don’t think there are any. So even if stone is more susceptible to earthquakes, it might still be the best choice for a building to last 1000 years.
