I used to play using a moveable anchor. It felt comfy to me and thought it muted the unwanted string enough. However, a few weeks ago I noticed by playing at higher volume that whenever I would move the anchored thumb (from E to A for example) the string I was moving the anchor from (the E string in this example) would start ringing, as if my finger bounced of the E string to get to the A. When anchoring on the A string, I didn't touch the E string anymore... I tried out some different methods to correct this like the moveable anchor technique from Adam Nitti where not only you anchor on a string below the one you play, but you place your thumb against the other lower strings as well. It felt very weird, probably due to my thumb shape. It felt like I had to bend my wrist to manage to place my thumb against the strings.
I decided to give the floating thumb. Well... that felt very very weird at first. And what a pain in the right arm/shoulder at the beginning, especially when playing the E string as it implies to move your arm more upwards.
A bit discouraging also at first because you have to get used to totally different plucking technique. I felt as comfy plucking as I did when I first picked up a bass
After a couple of days, I tried practising with a shoulder strap... well that was a tremendous improvement on the shoulder pain... sounds like a no brainer, why didn't I use a strap to begin with... 
After a couple of weeks practise, I already see tremendous results. I cannot play that fast yet, but that will come in due time. However, I notice much less fatigue in the right hand but also much more consistency in the way I pluck the strings. I didn't think anchoring the thumb was a problem but in my case I think I used to put way too much pressure on the anchor thus making my right hand slightly unbalanced. With the floating thumb, it feels comfy and relaxed. I kinda just wanted to use this technique to mute the strings better but it turns out the improvements goes much further than that!
It works great for me, and I am glad I gave it a try
Thanks a lot for all the info in this thread!!
I decided to give the floating thumb. Well... that felt very very weird at first. And what a pain in the right arm/shoulder at the beginning, especially when playing the E string as it implies to move your arm more upwards.
A bit discouraging also at first because you have to get used to totally different plucking technique. I felt as comfy plucking as I did when I first picked up a bass

After a couple of weeks practise, I already see tremendous results. I cannot play that fast yet, but that will come in due time. However, I notice much less fatigue in the right hand but also much more consistency in the way I pluck the strings. I didn't think anchoring the thumb was a problem but in my case I think I used to put way too much pressure on the anchor thus making my right hand slightly unbalanced. With the floating thumb, it feels comfy and relaxed. I kinda just wanted to use this technique to mute the strings better but it turns out the improvements goes much further than that!
It works great for me, and I am glad I gave it a try

Thanks a lot for all the info in this thread!!