The GH has the advantage that it is a 5 minute walk from 2 subway lines (Oedo and Hibiya lines). The Park Hyatt is a 10 minute walk to either the Oedo or Shinjuku subway line, and a 12-15 minute walk to Shinjuku station which has JR, Keio, Odakyu, and Seibu Shinjuku train lines and Maronouchi, Shinkjuku, and Oedo subway lines. But people on this forum often complain how far the PH is from transport stations, although the hotel does run a free shuttle to and from near Shinjuku station until 9:30pm daily.

Never been to the Andaz, I'll let someone else comment on that.