As a template fan and hunter, I’ve played a bunch of Biarritz holes, and though I preferred the all green versions at first, the Fishers version (uphill, with the front maintained as firm fairway) is my favorite - you can run a ball through as intended, and it’s beautiful.
The best modern version I’ve played is the 8th at Old Macdonald. It’s downhill, but the front portion of the green is slopes toward the back, which facilitates a shot that rolls down through the swale. It’s a terrific take on the concept updated for the modern game.
The 13th at Ohoopee is another great modern version with an interesting twist - the swale is green, but the “front” portion is fairway. So you get a bit of the best of both worlds.
I’m a big fan of the 9th at Yale architecturally. But I do think it’s a shame that they rarely pin it on the back section (I think I’ve seen it back there once in a dozen plays), and because the front tends to play a little soft. But I love the hole.
Ultimately, I agree that there is no single mandated way a Biarritz template should play. You have versions like Forsgate and Greenbrier with flat greens and big swales that don’t really allow for the running shot, but that have the added dimension of being pinnable in the swale. You have the all green versions like Yale, Chicago, Shoreacres, St. Louis, Westhampton and Camargo that allow 150 foot putts and a variety of different pin locations and yardages. And you have the half green, half fairway versions like Fishers, Mid Ocean and Piping Rock that will always be pinned in the back. It’s a versatile template design, and I like that.