If it hurts you to play with a "floating thumb" that's the one to avoid the most.
Anchoring on the pickup will probably let you apply less effort for the same sound, as you are striking the strings at a better angle.
I find anchoring on the pickup makes the movement across strings more complicated and slows me down, so I choose not to do it. You may find different.
If your thumb is not touching the strings at all, you have to mute the strings some other way. Some people mute with their left hand (I don't, because I have small hands and it's uncomfortable for me).
Choose the one that lets you play without pain and feels the most comfortable for you
