Let me first start off by saying that I am not extremely qualified to answer this, I dont know everything about the topic, but I can at least give you some insight.
Briar is a natural substance, therefore, it has, and can have, many flaws. A high grade of briar wont have any flaws, no fills no pits nothing. It should also have great grain, grain really serves no smoking differences in my opinion, but it makes for a pretty pipe. A high grade of briar should be, but doesnt have to be, pretty old. The older the briar, the more porous it is, the more porous it is the better the smoke will be. Older more porous briars will be lighter too, you can have a very large pipe that weighs almost nothing, many experienced pipe smokers will immediately recognize it by its weight as a good piece of wood.
When you wrap beautiful grain with zero flaws with an older more porous age, you will end up with a high grade of briar, and usually a more expensive pipe.
Dunhills are kind of a tricky explanation. First, they do use extremely flawless briar, even if they have a thought that there may be a flaw, and there turns out there isnt, they dont use the wood. Second, after they harvest the burl they age it for a long time, they dont say exactly how long, but some speculate about 50 years. Third they have a proprietary oil treatment process that is secret, that (allegedly) makes for a better smoke. You also pay for the dunhill name, and thats a big part of it.
Personally I do think dunhills smoke differently than other pipes, not neccesarily better, but different, worth experiencing at least.
I hope I gave you some help
John