Look up the density of air and, if you know the volume of the bottle, that will tell you the difference in mass - which will tell you the difference in ' buoyancy' (meaning how much the bottle can support). The upthrust will be the same in both cases, of course.
The buoyancy force depends only on the fluid that is displaced. It does not depend on what displaces it.
In your OP it is not clear if you are asking about the buoyancy force on something inside the bottle, or the buoyancy force on the whole bottle immersed in another fluid.