Fairy Dust Quest Guide
There is no difference unless you actually trigger an event after giving dust. I never was able to feed fairy enough so that it becomes friendly, but it worked with a first dryad after one try. She just gave me her loot and left. If you give a gift but she does not give you anything and battle continues I doubt loot will be different after you win.
Just continue progressing and you should get enough dust (you need just 3 if I remember correctly), don’t focus on completing that quest. I had more trouble getting dog’s and villager’s things for their quests in the first area when I was finishing it up, fairy one was completed quickly with just normal progression. Then I discovered that second area also spawns dogs and villagers so it was a waste of time to farm that loot in the first area and I could have just progressed further without waiting.
Also the final boss of the first area is a fairy and it seems she has 100% chance to drop all her loot as I defeated her once and she has full list in database (which includes fairy dust). Not sure if you have to defeat her in H-event for that or if it also works after normal defeat (I used H-event).
Note: Easiest way to finish this Quest is to use the 30F Boss before defeating her. Talk with her until she is willing to give you Items, get Items and then just find the Boss again and repeat until you have all Items.