The question is impossible to answer without additional information. Even assuming a sealed subordinate container with a volume of air and a volume of water (see Solomon Slow's comment), information about the heating method is needed. If we heat very slowly, such that everything in the insulated chamber is at thermal equilibrium with everything else in the chamber, the small addition of the heat capacity of air will make that chamber rise in temperature more slowly. If we heat rapidly, far from equilibrium, we might find the vacuum chamber's water boiling slightly faster (for instance: we shine a 63 GHz laser at the container), or we might find the air chamber's water boiling much faster (for instance: both chambers are convection ovens, but the vacuum chamber has no air to convect heat to the container).

The question is impossible to answer without additional information. Even assuming a sealed subordinate container with a volume of air and a volume of water (see Solomon Slow's comment), information about the heating method is needed. If we heat very slowly, such that everything in the insulated chamber is at thermal equilibrium with everything else in the chamber, the small addition of the heat capacity of air will make that chamber rise in temperature more slowly. If we heat rapidly, far from equilibrium, we might find the vacuum chamber's water boiling slightly faster (for instance: we shine a 63 GHz laser at the container), or we might find the air chamber's water boiling much faster (for instance: both chambers are convection ovens, but the vacuum chamber has no air to convect heat to the container, so the heating elements stay somewhat hotter and the water container remains cool for longer).