Why keep the same random draws?

Synthetic English narration.

Reuse the underlying shocks.
Common random numbers give each candidate parameter the same underlying shocks. Keep this simulated world fixed while comparing candidates.

New parameters, new outcomes.
Fixed shocks do not mean fixed outcomes. Change productivity dispersion, and those same shocks produce different simulated firms and a different model moment.

Change one thing at a time.
If every candidate instead gets fresh shocks, its moment changes for two reasons: the parameter and the simulated world. Reusing shocks removes that extra change.

Clearer comparisons, finite simulation.
Conditional on the fixed draws, we can compare parameter changes more clearly. Simulation error remains; averaging more simulated data sets addresses that separate source of error.