Interesting question. Purely empirically, it is the lift-to-drag ratio you are looking for. If you take this value as given for any particular aircraft, you have a direct answer for how much more effective wings are. It is the ratio of the lift to the total drag. The engine only needs to overcome the drag.
With L/D equal to unity you would need the same thrust as for the vertical take off. But even quite "bad" fixed wing aircraft would have L/D about 5. Gliders or similar aircraft built with a strong focus on aerodynamics can have an L/D of 50 or more (at least in some narrow range of airspeeds).
So yes, wings are more efficient. About one order of magnitude as a rule of thumb for common aircraft and optimal airspeed.
Why your reasoning with air pushed down is incorrect is more tricky to explain. I'll start with the assumption that, as air passes an airfoil, its speed relative to the airfoil is unaltered, and only the direction changes. (I know air slows down at least because of friction etc., but these are, at least theoretically, avoidable things not related directly to creating the lift. If there is something intrinsically related to lift which makes airflow change not only direction but speed too, then someone will hopefully correct me here.)
See the image. Airmass moving initially towards the airfoil with velocity $\vec{v_0}$ is deflected down by angle $\alpha$. Therefore the change in the velocity is $\vec{\Delta v}$. This change can be divided into horizontal and vertical components. To hold the aircraft in the air, the vertical component has to be equivalent to the aircraft's weight divided by the mass flow rate over the wing. The vertical component is related to the horizontal by $$ \Delta v_{\rm horiz}=\Delta v_{\rm vert} \cdot \tan{\alpha\over 2}. $$
So, from this simplistic view, the drag would be $\tan\alpha/2$ times the lift. Higher mass flow rate over the wing (longer wings, higher airspeed) makes it possible to keep the same lift with lower deflection ($\alpha$), thus less drag due to the generated lift.