I have stayed at the Green Park (actually I checked out this morning) and the Hyde Park (stayed there several times this year). I don't know about the Metropole.
Location
Hyde Park Hilton and Green Park Hilton are in a good location. Though I think the Hyde Park Hilton is in a slightly better location because there are really many (cheap) restaurants around the corner. Both hotels can be easily reached by tube from the airport.
Room
I stayed also in several other Hilton hotels in London. Some of them (e.g. Olympia, Kensington) have still these ugly, basic blankets on the bed. I never had a room in the Hyde Park Hilton with a blanket only. The bed sheet was always good. The room I had in the Green park Hilton had also a good bed sheet.
The Hyde Park Hilton has air conditioning and a fan in many rooms (maybe in all rooms?). The room in the Green Park Hilton didn't have air conditioning or a fan: it was already a refurbished room.
The rooms in the Hyde Park Hilton and in the Green Park Hilton are rather new which I rate as a big plus compared to old rooms.
Status recognition
Hilton Status recognition is very, very weak in London in general. Sometimes the Hilton Hyde Park supplies some water and chocolates, most times nothing. The Green Park Hilton offered water plus a fruit basket (3 apples + 3 strawberries).
Room upgrade is one category in both hotels: the rooms are rather small and basic (e.g. no minibar, but that is also quite common in many Hilton hotels in London.)
Public areas
Reception/Lobby area in the Hyde Park Hilton is quite basic while the Green Park Hilton looks quite stylish/nice. If you leave early (e.g. before 6am), the front door is closed at the Hyde Park Hilton. You have to call the receptionist with the telephone at the reception desk. It takes some time until he replies ... No problem with the Green Park Hilton to check-out and leave early.
I haven't seen a pool/sauna/gym at the Hyde Park Hilton or the Green Park Hilton. (I think a Living Well Centre is not far away from the Green Park Hilton which can be used as hotel guest. But I'm not 100% sure.)
I would go into the Hyde Park Hilton as the bed is excellent and the room is rather new. These are basic "requirements" that I would consider to be normal in most of the hotels. Unfortunately, I eperienced the contrast in many of the Hilton hotels in London with these old blankets and old rooms. I learnt to appreciate the Hyde Park Hilton ...