Dreamer, these are the basics of it..
Clay (terracotta) roof tiles generally have better fire resistance than concrete roof tiles, because they're burned at high temperature..
Clay is also a better at preventing the transfer of heat and sound because of its light weight..
On the other hand, concrete tiles are cheaper than clay tiles, and come in more attractive colors than clay..
But with time, clay will be less vulnerable to damage by weather conditions compared to concrete..