This is actually a super hard fluid dynamics problem.
The diameter of the top vent only matters if it becomes small enough that a pressure differential is created which results in reduced flow of water out of the tank
A simple analysis is that water leaves the tank with a volumetric flow rate of V_w m^3/s and air flows into the tank with a volumetric flow rate of V_a m^3/s.
If V_w ~ V_a, the flow rate is driven by gravity and you get the maximum flow V_w_max.
If the diameter is small and V_a << V_w_max, you get a pressure differential that limits flow. If you ignore effects like air flowing in reverse up the water vent, you can model the flow rate as min(V_w, V_a).
Now where this gets interesting is that any modeling based off ideal gas conditions will show you that V_w == V_a and the vent diameter doesn't matter.
To actually get a sense for how the air vent diameter impacts flow, you need to model the system as a real gas with non-stationary flow and pressure dynamics inside the tank and at the air vent.
