Greg,
I use/have used all three papers you mention over the years as well as Bergger Cot (in both weights).
As you suggest, these papers are all quite similar, but there are some very subtle differences. So subtle that, I think, you would only notice the differences in a careful side-by-side examination.
My observations...
Hahnemuhle Pt Rag is the brightest white, the others are all quite white but just a tad warmer.
Legion Revere Pt is the smoothest, the others are also quite smooth but have just a bit of tooth.
The biggest difference is that Arches Platine and Bergger Cot are available in a lighter weight version as well as the 300ish gsm versions.
As for my practice (mainly salted-paper and some platinum/palladium), I currently use HPR and Revere Pt interchangeably.
I find HPR a bit easier to procure (I buy 22x30 inch sheets which I cut down), but that is really the only advantage it has for me over the Revere Pt.
On rare occasion, when for instance, I am going to tip prints into a book, I will use the light versions of Platine or Bergger but that is not very often.
I hope this is useful,
--- Frank