Stayed at both last summer and liked both. The "hard product" at PP is really stunning imho and beats GhedM easily.
(When we have been there the SPA / Pool wasnt open yet, so no comment on that, but I guess it didnt turn PP for worse...)
We had 1 dinner recommodation from the PP concierge which satisfyed us.
Breakfast in their lovley garden... awesome !

We had a junior suite at the GHedM which I think was a very good mix of old and mondern elements.

Locations wise its a win for GHedM which is directly at via Monte Napoleone. PP is about 500meters away. We didnt mind the 5min walk...
( I guess if it would be moved 500m closer to duomo / shopping it would be same price league as MO,FS, Armani Bulgari etc...)

I would go for PP, which gave us a "wow" couple times but it wasnt really that there was something wrong with GHedM.

PS: I heard the Restaurant at PP isnt as good as the rest of the property... we didnt try. I think they had a guest chef from somewhere end of last year/ beginning 2016... no clue what the actual situation is like.