Onagers and Heavy Onagers:
Stone against walls for best damage. Burning buildings is pretty useless unless you can hit the palace and your intention is to leave the city a wreck. In that case, Breach with stone, Flame Balls to burn the palace and then kill all the towers you can with remaining stone.
In the field, I mostly use Flame Balls. Accuracy is poor against a moving target or a target that's adjusting lines frequently. So make each hit a blast.
Caveat: If you are firing along the bias of a unit, down the length of a bridge or some such -- where the skipping ball can whack many in a given file -- then stone is slightly more accurate and generates more kills. Against blocs, the Flame Balls kill more.
Ballista, Scorpions:
Almost always use stone. Not much "blast effect" from these, so bouncing stones/bolts for multiple kills is the way to go.
Shieldmaiden is correct as to the best mobility for onagers. Works well save for Russia.
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