As an explanation of wing lift, I prefer the downward deflection story. This explanation can be explained with other experiences with fluids. A swimmer propels themselves forward by pushing water backwards. An airplane stays up by pushing air down. If you hold a flattened hand out of a moving car and tilt the leading edge upwards, you can feel the wind hitting the bottom of your hand, pushing it up.
This is not to say that the pressure story is false. The air pressure above the wing is in fact lower than below the wing, but it can be difficult to explain why there is a pressure difference. If you say that air flows over the wing faster than under the wing, this just raises the question of why there is a difference in flow speed. Answering that question is complex.
Both explanations are equivalent (as they should be, since they describe the same phenomenon). Air is deflected downwards and the air pressure is higher beneath the wing.