I regret to say that in the US “ordinary people” probably have no occasion to use either. Americans’ knowledge of even their own geography is extraordinarily poor.
I’d be willing to bet that if you picked ten people off a US street and asked them to name all the Chinese cities they’d heard of you’d get three: Beijing (older folks might say Peking or Peiping), because they hear that regularly on the news, and Shanghai and Hong Kong, because those show up in lots of movies. Perhaps the generation which went through WWII will know more; but there are very few of them left.
In any case, what you want to look at it is not what’s in books, but what’s on the news; and I think most broadcast, cable and internet sources use the Pinyin spellings these days.