Geez! I've missed you people!! I guess I got busy having grandkids.
Let me take a shot at clarifying the distinctions, as I see them, between a Biarritz and a Double Plateau. Most of this discussion is limited to Biarritz greens versus Double Plateau greens. I live near Philadelphia and I get to play a hole with a couple Double Plateau greens just about weekly at Lederach (#4 #11). They're both par 4s playing into green complexes that are oriented differently... the fourth like a Biarritz with the swale bisecting the green, perpendicular to the line of flight on approach and the eleventh with the swale bisecting the green on an angle such that the back tier is like that twisted piece of taffy... maybe 35 degrees left of the front plateau. In my mind, these both qualify as Double plateau greens though I think it only proper to respect the original question as it had to do with double plateau and Biarritz holes which are invariably par threes.
I missed getting to Yale this summer (again) so I've yet to see what folks generally call "the best" but I've played a few Biarritz holes in my time. There's a weak sister (It's sort of like this.) at McCullough's which is a poor man's architectural tour of some of the best that England, Ireland, Scotland, and France (in this instance) had to offer. Another, better example of a Biarritz design exists at Forsgate's Banks course #17. My sense is that Biarritz holes have at least three defining characteristics: the significant swale oriented perpendicular to the ball's line of flight, the chasm (or significant hazard symbolizing the chasm that the Dunns built over at La Phare), and the length both of hole (typically in the 190 to 235 yard range) and the green itself (typically in the 50 to 80 yard range). I suspect that a lot of superintendents (Guys... correct me if I'm wrong on this!) didn't like maintaining the front tier as green when the pin was back 95% of the time so front tiers became fairway and swales became false fronts.
So far as I'm concerned, there are lots of double plateau greens / holes. There are triple plateau greens as well, some of which come with windmills and clown's noses. I think most people reference greens that have multiple pateaus (I also like the spelling plateaux.) without much regard for the conformation or strategy of the hole itself. My inclination is to respect that classic design from the original Biarritz forward included "the Biarritz" as a type of hole that was repeatedly replicated but greens with two plateau areas are just complicated green complexes... not really a type of hole like the Eden, Redan, or Biarritz.
I do respect that Brian Silva in a great article for Links Magazine referred to the St. Louis CC hole as a "Biarritz". Everyone has an opinion but I think "challenging putting surfaces" and "classic golf holes" are two different things. JMO.