Andaz 5th Avenue feels more like a hidden getaway boutique hotel, while GH is, well, grand and large.
Andaz has a better appointed bathroom, if that's important to you. At GH, it's luck of the draw in terms of amount of counter space available.
As a diamond member, Andaz offers $15 credit or 1000 points for diamond amenity. GH offers the typical bottle of wine + small bites. Andaz offers up to $75 for breakfast, including room service, while GH offers the lounge option with breakfast and evening hors d'oeuvres.
GH charges $2 for luggage storage, which is waived for GP elite members.
+1 for Andaz.