Hi jkdoctor, welcome to FT and the Hilton forum. Hope you enjoy your stay in London, regardless of which hotel you choose. ^ Please do come back afterwards and post your comments so you can feed back your experience to help others!
I've not yet stayed at the Metropole but I have stayed at the Westminster DT.
If this is your first time to London with your family and you are able to book two rooms then I would certainly suggest the DT Westminster is the better of the two choices you asked about.
It is closer to the main tourist sites and you could walk to many of them without needing to take the tube (potentially saving quite a bit of money if you are here over a few days).
The Westminster is very central but still quiet as it is tucked away a few streets from the 'action'.
The rooms in Westminster are very clean and modern and you will find it very functional but quite small so definitely need two separate rooms. If you want to try to get 4 people into one room using 2 double beds then don't consider the Westminster location as the room would be too small for 4 with your luggage for more than a quick stopover between flights.
The breakfast is great here and is one of the few DT's in London where it is not overcrowded. ^ (it is popular and busy but not anything like the other DT's in London in terms of crowds).
I imagine the Metropole will be a bit more impersonal simply due to the size but some bigger hotels still do great personal service. You will likely find the Metropole better for room size but still a challenge if you want to put 4 people in one room with big suitcases.
The location for the Metropole is a bit further out so you will be using the tube (subway) quite a bit but still within reach of any sites in London within a few minutes really...
Hope this helps, if you have any specific questions please do post as it will help others to add to the comments about which to recommend. You'll appreciate that one family wants to see the sites and another may simply wish to enjoy sitting around the immediate area and use any hotel services such as a pool or such...so details you can provide on what you wish to achieve help to provide insight. (first time visit? looking for peace and quiet or wanting to see the lights and sights...etc,)
As mentioned, enjoy, its a great city.