The difference between the explainations are because aeronautical engineers and physists are looking for a theoretical model that allows them to calculate the amount of lift a given airfoil will produce under a given situation - which is handy if you are designing an aircraft.
That is why they "complain" about the Bernoilli explaination of lift - it is difficult to apply Bernoilli's equations (developed for fluid flow in tubes) to freestream airflow over a wing, and calculate the amount of lift the wing will produce.
As pilots, we really don't care about that - we want to know how the wing will react in flight to changes of angle of attack, camber (flaps), damage, airspeed etc etc. The "Bernoilli explaination" allows us to set up a reasonable (albeit simplified) mental model that permits us to intuit the wing's response in flight. That is why it is by far and away the most popular method taught to pilots to "explain" lift. It's an instructor thing - instructors who rattle on about circulation and newtonian physics may be presenting a more accurate picture - but their students will never be able to build a mental model useful in flight from that explaination (evidence the post above).