One potential advantage is in uniformity. I used to drop my bullets onto a damp towel, but it's rather obvious that the side that touches the towel cools faster than the side that does not. Also the spots that touch the towel often take on a texture of the thread pattern, while the other side remains smooth, I didn't like that, either.
So now I usually water drop. Appearance is definitely more uniform, and I assume the cooling rate is, as well. I do it mostly to get the uniform appearance, if there is a functional difference I have never noticed it.
Answers about hardness should come with a big asterisk. Lead alloys don't quench harden, but they will precipitation harden. Precipitation hardening has 3 distinct steps:
- Select alloying elements dissolve into the lead at high temperature
- Rapid quenching traps the alloying elements in the dissolved state (not a natural or stable condition, as thermodynamically they should occur as independent phases within the lead matrix)
- With time, the elements precipitate out of solution to form millions of tiny islands in the lead. It is these islands that increase the strength and hardness of the material.
The problem occurs at step 1. Much of the time when casting, we aren't opening the mould until the temperature has dropped below the dissolution temperature, so some or all of the alloying elements have already come out of solution to form independent phases before the quench happens, instead of trapping the necessary elements in a dissolved state. Or, due to variations in casting technique maybe sometimes you trap the elements in solution, sometimes you don't, with resultant variability in how much hardening can happen.
This is why it is more effective to reheat the bullets in a separate step, hold for a few minutes to ensure dissolution, then quench.