City Raider will result in more damage to the toughest unit in the stack.
Collatoral Damage will result in more damage to the units other than the toughest.
That's all you really need to know. As a rule of thumb use Collatoral until the city-rader promoted siege weapons actually have a good chance of winning (say 35%+).
Note that Catapults have no (defensive) counters, unlike Swordmen (axemen) and Horsemen (spearmen), making them pretty good at city siege despite their lower strength. Cannons simply rock, a Raider3 cannon will destroy anything in the era. Artillery can be good too if you get them quickly enoungh.