I go back and forth and back and forth on this issue. My early years of playing guitar, from the age of 12 to about 16, I only ever used a flat pick to play the guitar. I rarely finger picked. Then, when I started to learn solo jazz guitar at 16, I started to use a flat pick in conjunction with some basic finger picking with my middle, ring, and pinky fingers. A few years later, I got really into playing classical guitar and some basic "fingerstyle" guitar. Then, eventually I sort of stopped using a flat pick altogether and just finger picked.
Then, I saw Tommy Emmanuel in concert and everything changed. After I stopped myself from burning all my guitars after that show (a common reaction for guitarists after seeing TE play live for the first time), I decided I should ALWAYS play with a thumb pick because TE had just changed the world of guitar playing and he played with a thumb pick. I did this for a few years, but I never really liked it. It's certainly louder and creates a more powerful sound. It also very much makes it sound like two guitar players playing at once. But it sort of slowed me down and I felt kind of disconnected from the guitar. Also, I've gotten very used to the mellow sound of just fingers with no pick.
The amazing thing that Tommy Emmanuel does that I've never seen anyone else do is that he uses the thumb pick to play his bass lines, but then he also can use the thumb pick just like a flat pick. It's amazing if you've never seen or heard him do this. I really wanted to learn how to do this, and I did, but it has always been a little clumsy.
So, as of right now, I don't use a thumb pick. You can probably find some older YouTube videos of me playing with a thumb pick, but as of right now, I'm not using one. It feels a lot better to me to just use fingers, but I've had to let go of one big thing: Stop trying to be Tommy Emmanuel! There's only one of that guy and no one else can compete with him on being him. He's a one of a kind, like all great guitar players, and you can't be someone else. It feels very good and very freeing to let go of that. Trying to compete with Tommy Emmanuel on guitar is like thinking you're going to beat Michael Jordan in a game of one-on-one. It ain't gonna' happen in this universe or any other dude. It's a lot better for me to just play the guitar the way that feels right for me and not worry about how it stacks up compared to anyone else.
So, that's my answer right now. It helps that I recently realized that I can use my index finger fingernail as a flat pick and can play fast flat picking runs that way while still having the ability to finger pick. Holding onto a flat pick makes it a lot harder to do any actual finger picking beyond basic "plucking" for me. Carl Perkins and George Harrison could do it, but if I'm going to finger pick, it's easier to not be holding on to a flat pick. Also, the sound of a fingernail on the strings sounds a lot more organic and "real" to me than the sound of a plastic or tortex pick. I've gotten used to that more "organic" sound I guess.
Anyway, that's what I'm doing this week. That might all change by next week.