As my new gas water heater heats up, I hear dripping and a sizzling sound when the water hits the burner. The plumber says it's condensation due to cold weather, but this never happened with my old unit. Regardless of the weather, a new water heater with a clean tank and cold water entering at the bottom tends to form condensation until the tank warms up. The moisture often falls onto the burner and creates the sound you describe.
Excess condensation collects in a small pan in the heater and soon evaporates.
The reason your old unit was silent is that a thick layer of sludge probably insulated the bottom of its tank, preventing condensation from forming and dripping onto the burner.