To settle this question, let us do some hydrodynamics. I will do static and quasi-static hydrodynamics only, to make it easier.
First, the pressure-equilibrium equation.
where P is the pressure, f is the force density, (rho) is the density, a is the acceleration, and V is the potential.
For small distances h and acceleration of gravity g,
For centrifugal acceleration at distance r from a central axis with angular velocity w,
Density is related to pressure, temperature T, and molecular weight m by the ideal gas law:
Non-ideality is usually small enough to ignore without loss of much accuracy.
The pressure-equilibrium equation and the ideal gas law are two equations for three quantities, (rho), P, and T, so we need a third equation.
I will consider two types, a power-law adiabatic,
and isothermal, T = constant.
Adiabatic first, since that is essentially convective equilibrium, equilibrium over moving up and down. It is easiest to find the temperature, and from the power law, we have
Plugging it into the hydrostatic-equilibrium equation gives us
giving us
For the gravity case, we get
(Gamma) is called the "adiabatic lapse rate".
The Earth's dry adiabatic lapse rate is 9.8 C / km.
One can do similar calculations for the centrifugal case, and the center-to-rim temperature difference is half that for constant acceleration = rim acceleration. Thus, if one has 1 g at the rim, then temperature difference between the center and the rim is 4.9 C / km * (radius).
So there won't be very much difference unless the habitat is very large (radius ~ several kilometers).
Now the isothermal case. It has
giving us
and
Here also, detailed calculation does not show much change in air density unless the habitat is very large.
Returning to the OP's conundrum, if the hub gets an air leak, the entire station's air will leak out unless the station is divided into sealable compartments. For a large station, I think that such compartments will be a necessity.
I suspected that might be the case. A small (ie less than tens of km diameter) space station is essentially at similar risk of decompression regardless of spin gravity - the rotation helps people at the rim to live in earthlike gravity, but does little to protect them from any kind of serious atmosphere leak, even at the hub.
Which is probably a good thing in the absence of a leak, as it allows workers at the hub to breathe without spacesuits. If an uncontained hull breach at the hub was a minor problem for those at the rim, then working unprotected at the hub would be impossible.