Anyone here who participates in sailboat racing will know that technically-oriented racing sailors love to debate this question almost as much as pilots do. In fact, the second-fastest way to provoke a shouting match at the yacht club bar after racing, is to bring up the pressure difference (Bernoulli) vs flow deflection (Newton) theories of lift.
The two theories are not competing explanations at all -- they represent two different ways of talking about exactly the same behavior by the air molecules involved. The two explanations are inexorably linked together. The only way for the pressure above the wing to be lower than the pressure below the wing is if air is being shifted downward. So it makes no sense to argue about whether it is the pressure difference or the downward deflection of the air that creates the lift, because one cannot have one without the other.
(as an aside, this is the second fastest way to provoke a yacht club brawl because it'll never surpass asking, with feigned innocence, "Say, which do you think has lower drag, a hull with a mirror finish on which water would bead, or the same hull with a matte finish on which water would form sheets?)