I don't think there's a comparison thread, but I can tell you that calling a hotel in NYC a PH or GH or Andaz doesn't matter. I think they use the designation due to price.

There's nothing grand about the GH NYC. I'm not familar with the PH or Andaz in midtown. The Andaz Wall Street is so-so, IMHO.

If you want true luxury, you have to go to the Ritz or Four Season, or a host of other higher end hotels.