OK, here are the only ones I visited and would dare to comment on. Note that much has likely changed since I was last at those places. (X) means I have been there X times.
England:
Bovington, SW coast, absolutely essential for any treadheads. (3-4?)
Duxford, Midlands, more tracked toys but more aircraft (1)
RAF Mus. Hendon, NW London (1)
HMS Belfast, central London (1)
Imperial War Mus., central London (2-3?)
The first three are suitable for a long day visit to get your effort's worth. With the IWM, you might be best to do a quick visit to check it out then pick one or two themes and later do a full visit. HMS Belfast while well worth a bit longer, could be done in 2-3 hours. There is just so much to see, a couple of hours simply won't be enough for most people, Belfast excepted. The IWM just covers so much stuff, you need many visits (and Duxford has a lot of IWM hardware).
Germany:
The Munster armour museum, about an hour south of Hamburg. (1)
The various antiquities museums on Museum Island, Berlin. (1)
For Munster you should set aside 3-4 hours, more if you're a treadhead or modeller. Not quite as much as Bovington, but enough for me to flag by then end. Museum Island could last you a week. With a Greek temple hijacked from Pergamon, Ishtar Gate from Babylon and the Nefertiti bust, the Germans made the British antiquities looting look amateurish.
I can recommend all the above without hesitation and I'm not a museum visitor. Museum Island particularly impressed me.