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I haven't been a headphones person since high school, perhaps my early 20's when the only mobile music I or anyone really had was a portable CD player which only came out for road trips. I had a boombox for at home listening.
I did have a pair of wireless headphone a couple of years ago but they were a Christmas gift and the charger crapped after six months. Again, those never went out in public.
Ergo I have no experience with their soundproof nature in public.

Earbuds became preferable to me because headphones would make my ears sore after a short time.
Specifically hanger earbuds otherwise they won't stay securely in my ear.
At the moment I have BT250 Bluetooth earbuds that have internal sports hooks rather than hangers but as long as I don't move around too much in them that's adequate. I've not seen wireless earbuds in hanger style yet.

I'm a tad self-conscious about the sound of my music traveling out of the buds as well that's why I keep my volume as low as I can without impairing my own hearing.