None as far as we know, sandy. Chaucer uses the phrase twice in Canterbury Tales, describing the colour of a horse. As to which berry he meant, only he knows. Perhaps he was red/brown colour blind?
Then why didn't that there Chaucer feller say "as brown as a dried berye (sic)"? Instead of having us all looking for berries that are brown when they are 'alive'. Mugging us all off, he was. Thinks he's clever just 'cos he wrote a book.