The situation in the U.S. is very different to the U.K.
I understand that Phillips screws were used widely in the U.S. almost since their inception, and certainly on anything mass produced! As stated in the links above, they were designed to 'cam out' when operated with powered drivers on assembly lines!
Pozidriv screws were designed not to 'cam out' (pozidrive being an abbreviation of 'positive drive') to be used in the torque controlled drivers that were introduced in the 60's. They are much nicer tools to use as you don't have to lean on them so much. Better for hand tools too! Unfortunately, folks were so used to Phillips by then, that the Pozidrive never really took off in the U.S.
In the U.K. it was different. Although there are a few cars from the 50's where you will find Phillips screws, they were generally the preserve of the aviation industry. Just about every post war British airliner from the Viscount through the VC-10 and the 111 right up to the 146 and every current Airbus use Phillips screws. Nobody else did though!
I seem to recall (it's going back a bit now) that the Pozidriv was licenced to Nettlefords (later GKN) Britains biggest screw producer, and it was pretty much an instant success! It was adopted by many industries and you will find Pozidriv screws on just about any British made product from cars and bikes through to electrical equipment, machinery and domestic appliances. They were used in some places where they probably shouldn't too! British Motor Corporation cars from the 60's and 70's often have their door hinges secured by several short No. 4 Pozidriv screws!
Nettlefords started selling wood screws with the Pozidriv recess too, and I can remember my Dad coming home in about 1969 with a boxed set of screws that included a free driver (which I still have)!
Pozidriv is pretty much the British and European standard now, and I hardly ever use a Phillips unless I'm working on something U.S. made, or Japanese (or aerospace)!
Like many Brits faced with such a choice of screws I do try to keep my drivers colour coded to prevent confusion! My normal and Phillips tend to be red or black, Pozidriv blue or green, and Torx yellow or orange! Now, what colour was that Tri wing...