Good briar is briar that grew 2222 years in an Elvin forest protected by beautiful Dryads. The briar cutters do a dance known as the "Mamushka", prior to attempting to harvest any wood. Ritual sacrifice, prayer, displays of bravado, etc. When they find the 2222 year old plant, they dig it up, cut it in five equal pieces, and go home. It's a very strange thing. But miss any step, or issue the wrong chant, and the briar goes bad.
For real, here's the best "process" video I know, from and featuring the Greek Devil himself, Makis Minetos. Video starts with freshly harvested burls, which have been selected off the mountainside of protected/controlled areas in Greece. Burls old enough (which is simply to say large enough) and of sufficient physical qualities (lack of cracking, insects etc) have been chosen. After that, it's up to the mill.
And this process is repeated at every mil, there's really no variation I know of, some guys might swap the water out more often, but the answer is briar is harvested, cut, boiled, graded, and put aside.
Just what makes "good" briar might depend on a more specific purpose. If you think light briar smokes better than heavier briar, then there's your answer. If you want incredible striated grain, then there's your answer. If you want briar that sandblasts a certain way, which is to say, the rings are a certain distance apart because of growth conditions, there's your answer.
I buy lots of briar from all over, I've had wood from Spain, Italy, Algeria, Greece, Albania.... and there's better and worse pieces, some have cracks, some have no grain, mostly you get what you pay for in terms of grain (and that's what cutters charge for, grain density, how flashy is this piece going to be). But in terms of other mystical characteristics, how "good" it smokes etc, I don't really think anyone has a firm, non bullshit answer about that. If I could buy only "good smoking" briar I suppose I would, but a better way to state it is that I've bought all kinds of briar and find it all "good smoking" with only really marginal differences to demarcate different provenance.
If someone says "I want a pipe to smoke Virginias" I have no secret supply of tried-and-true virginia smoking briar.
Bad pieces of briar look like this, for example... look at all the cracks running through it. And the color variation kind of freaks me out too, like what mineral did this plant grow on? That's a fail.
Good briar is .... not like that.
That's a nice clean piece, I don't care if it's Spanish or Greek, or if it was picked at midnight or if a unicorn pissed on it. It's not the
straightest grain I've ever seen, but it's a good
quality of wood.