Different weapons does have different luck on them, for both elixirs and stones. Each weapons have a chance of success in elixirs, at each level. For stones, the chance of putting the attribute on depends sololy on the stone, but the % of the attribute once succeeded depends on the weapon itself.
For example, I once used a weapons that have 18% critical. I modded the critical, and it changed to 0%. I repeated this 4 times more, and out of them 2 succeeded. But both times, the % changed from 0% to 0%.

So in 3 successes, the critical all goes to 0%. So the % of the attribute depends on the weapon.
Characters have no different luck. Everyone have a certain chance of getting an item drop, and out of them some are SOS.