Food for thought- how does a wing create lift? Do the Bernoullis in the air push harder on the bottom of the wing than the top ones going faster? Or does the wing push the air down and the Newtons in the air push the wing back up? (Answer: sorta both)
There's a lot of discussion at APC about the whole lift thing. From my understanding, the common ground between Newton and Bernoulli is in the Conservation of energy, mass and momentum. Bernoulli is all about the conservation of energy, while Newton is all about the conservation of momentum. All of which work of similar principles and can lose relevancy to one or the other (i.e. viscosity, compressibility,etc). The generation of lift is pretty complex, and it's hard to really have an accurate simplification.
There is a lot of BS out there though, like the 'equal transit theory' and 'venturi flow for lift' model.
One interesting note is that Bernoulli studies and principles were a function of an incompressible fluid, like water. So each have their relevancy under a certain set of conditions.