We debated that extensively about 8 years ago, and again about 4 years ago. There is a single variety in GRIN that is identified as "Perique". A number of us have grown it. To my eyes, the fully grown plant looks to all the world like Hickory Prior (a flue-cure variety). Some of the old literature seems to indicate that the Louisiana Perique is a descendant of a red Burley (not a white-stem).
FmGrowit made some Perique from a burley variety, and it was pretty damn close in taste. But others of us have made Perique of dozens of different varieties, and many of them come close, as documented in a blind taste test undertaken by Jitterbugdude. The pH, flavor and aroma seem to be determined mostly by the process, whereas the nicotine strength of it is dependent on the tobacco variety used.
Bob