I assume you are talking about MURS. Regardless, narrower is always better for weak signal reception. It's a physics thing, the frequency is irrelevant.
From a transmitter perspective, you can have the same amount of power spread across 20kHz bandwidth, or spread across 11.25kHz bandwidth. Spreading that power out over a wider bandwidth means the peak power at any instant is lower (since it is spread out more).
From a receiver perspective, you can receive the same amount of transmitted power, along with the noise power that exists within 20kHz, or 11.25kHz. The narrower the bandwidth, the less noise you will receive along with the information that was transmitted.
From both perspectives, narrower is better for weak signal reception or in noisy environments. The tradeoff of using a narrower bandwidth is the amount/speed of information you can send being less, which takes a toll on audio fidelity/data transfer rates.
Disclaimer: There is no guarantee this next part would work in your situation.
One thing that I have always wanted to try for a situation like that is to cut a half wavelength horizontal slot in the metal siding on the side facing the desired direction, and to cover that slot with duct tape. Depending on the distance between buildings, the slot antenna (vertical polarization for a horizontal slot) should capture and re-radiate some of the signal and create an RF window on that side of the building. Whether or not enough power will couple through the slot, I couldn't tell you, but in theory, it should act like a passive repeater but better since no lossy coax is used.. I recommend trying on someone else's shed first lol.
