Maybe bass audibility for neighbors deserves a separate branch. Or does such a thread already exist?
Given a certain sound pressure level at the primary listener's ears, a higher directivity (cardiod) reduces the diffuse field, logically.
A lower diffuse field will reduce the grand total sound leakage through the walls, naturally.
Of course the desired effect depends on which wall separates the secondary listeners from the sound field.
As always it's complicated.
One word of caution: a higher directivity will reduce room interaction, means lesser reflections from boundaries. But is that feasible? Below the Schroeder frequency one wants as much reflections as possible, because the wider distribution of reflections will fill in nulls and cut peaks towards a smoother pattern of so called resonances. (Often forgotten, when discussing directional woofers.)
From a practical perspective, the transfer through the house's construction depends not only on the walls' isolated (isolating) properties. One can have nasty leakage paths, barely predictable, from a single reinforcement bolt somewhere. A single frequency might travel without attentuation down to the basement, and every other are quiet. So, resonances are the worst to have. You see the conflict? Higher directivity probably raises singled out resonances**, while resonances are the main contribution to sound leakage. Also reinforced by the hefty non-linearity of the ear's sensitivity towards lower frequencies.
An anecdote because this is DIY. Speaker enclosures--what many people think is enclosure wall resonance is actually the resonance of the air inside the cavity, that sound traveling through. I proved it practically and theoretically. And some other too. Of course this enlightment was discarded by the community, as they always do.
** not necessarily at the listener's ears but elsewhere, where it still might find a path to the neighbors.