It really depends on the blend that you're smoking, IMO. But, yes, I taste a difference, but not just in the briar, but also the pipe design. For example, Virginia #1 is more intense in a tall narrow chambered pipe, whereas in a wide pot shaped pipe, it mellows out and loses a bit of it's bitey-ness, and has a richer deeper taste. Also, I notice a difference in pipes with a thick amount of brair surrounding the bowl, verses a thin walled pipe.
However, on the briar itself, I notice that my Savinellis have a more twangy taste to the briar. It is very subtle, very very, but it's there, whereas my Ferndown and one of my Beckers has no taste at all, as if it was cooked out of the briar. I also have a few very old briar stummels (+100 years) that I used to make custom pipes for myself with, and they the most mellow aromas, which seems to have shifted as I use them, getting better as I smoke them.
I did get a Peterson about a year ago that had a very green taste to the briar. Although I have heard that this is not the norm, probably a fluke, but it made me sort of sick, with it's cloyingly sweet green taste to the wood. It was probably not aged or something.
But, for the most part, there are differences. I don't think that there is one taste for any particular region of briar harvest. I don't exactly know what effects the different tastes, but I enjoy discerning the differences. Also, the briar flavor changes as you use the pipe, probably driving out the oils of the wood and adding the tars and bi-products of smoking to the wood. IDK, just a guess.
But, yeh, I notice differences in tastes.
That said, if you are smoking aromatic or latakia blends, you may not notice. Maybe I notice because I prefer very light Virginias, which have a very subtle flavor to begin with.