I don't thing British "chose" a German/Dutch word, it was the native choice. We speak a Germanic language, though it has been quite influenced by French and Latin loan words. Faucet sounds like a much "posher" word to me, native British English speaker.

I think this is a common theme. British English has earthier words, American English seems to have fancier terms in a lot of cases - but sometimes it is reverse. Pot luck really, though I think AmE is the fancier one for general terms. The one that always sticks in my mind is the AmE "transmission", which is in BE, "gearbox". I wouldn't know what "transmission" means if someone hadn't told me, but I could have worked out what gearbox was from the fact it was talking about gears.