IME, each of a badger, boar and synthetic can produce a very usable, and enjoyable, lather. Each has its process, which ultimately is to load the brush with the appropriate amounts of soap and water, in the right proportions. To do that right is simply a matter of trial and error; and gets easier with experience.
After that, it is a matter of preference. For me, I can describe each category as follows:
Boar has the feel of a paint brush.
Badger, especially a dense silvertip, has the feel of a perfect sponge.
Tux synthetic has the feel of a sponge too, though, as its name implies, a synthetic one.
I share the preference of the OP, but have to say the Yaqi tux is shockingly good.
After that, it is a matter of preference. For me, I can describe each category as follows:
Boar has the feel of a paint brush.
Badger, especially a dense silvertip, has the feel of a perfect sponge.
Tux synthetic has the feel of a sponge too, though, as its name implies, a synthetic one.
I share the preference of the OP, but have to say the Yaqi tux is shockingly good.