The answer to your question depends on a full analysis of the system, not just the
f/number alone.
The first point is to correct two common misunderstandings which, unfortunately, are
repeated in other answers to your question.
f/number is not the aperture. Aperture is the actual diameter of the lens opening viewed
from the front of the camera. f/number is the ratio of focal length to aperture.
The product of aperture (not f/number) and angle of view determines the total amount
light captured. This is the key to image quality.
A camera's ability to gather light is the predominate factor for determining performance
in low light. All things equal, extra light gathering reduces image noise, allows more
flexibility, such as faster shutter speed for motion capture or lower light shooting. For the
same angle of view, the light gathering ability of a camera/lens combination is
proportional to aperture area.
The second point is to understand the relationship between the camera/lens parameters
of aperture, focal length, and sensor size to the image parameters of field of view, depth
of field, and image noise. Let's compare a few typical smartphone cameras:
LG G4: An f/1.8 lens, 28mm equivalent focal length, mounted on a 16MP, 1/2.6 sensor
(5.79 mm x 4.01 mm). 16x9 aspect ratio. Crop factor 6.14.
Apple iPhone 6: f/2.2 lens, 29mm equivalent focal length, mounted on a 8MP, 1/3.0
sensor (4.89 x 3.67 mm). 4x3 aspect ratio. Crop factor 7.07.
Samsung Galaxy S6 Edge: f/1.9 lens, 28mm equivalent focal length, mounted on a
16MP, 1/2.6 sensor (5.79 mm x 4.01 mm). 16x9 aspect ratio. Crop factor 6.14.
The actual aperture size of each is found dividing the equivalent focal length by the
product of the crop factor and f/number. For these three cameras ...
LG G4: Aperture = 28/(6.14*1.8) = 2.53 mm
iPhone 6s: Aperture = 29/(7.07*2.2) = 1.80 mm
Galaxy S6 Edge: Aperture = 28/(6.14*1.9)) = 2.40 mm
On this basis, the LG G4 has roughly 2 times the light gather capability as the iPhone
6s. On that basis the LG G4 would be preferred.
Next consider depth of field. The actual size of the aperture determines the degree to
which background is blurred when seeking that effect. On that basis the LG G4 has a
small advantage over the other two. It definitely doesn't compare to larger cameras
where a lens aperture of 10-20mm is pretty common. You don't use smartphone
cameras for shallow depth of field shooting.
For some situations you may want a deep depth of field. Again aperture is the key. For a
camera focused on a distant object, the minimum resolvable detail in the foreground is
equal to the lens aperture. For this case the iPhone has a small advantage.
Finally, consider lens quality. This is much harder to predict because lens design is a
complex matter. Things like quality of the lens elements, ability to control flare and
distortion are paramount. For that you have to look at detailed lens testing reports.
A fundamental limit on resolution is due to diffraction of light passing through an
aperture. For red light of 750 nm wavelength at f/2.0, the minimum resolvable pixel
(using the Airy disk formula) is about 1.22*0.75*2.0 = 1.8 microns. The 16MP sensors
have a pixel size of 1.2 microns, and the iPhone sensor a pixel size of 1.5 microns.
Therefore, even if the lenses were perfect and diffraction limited, these cameras can't
quite resolve 8MP (much less 16MP) of image detail. More MP don't make much of a
difference once you're past about 8MP. Light gathering, lens quality, and diffraction
limitations have far more to do with image quality than megapixels.
Dynamic range refers to the ability of the sensor to record a wide range of tonal values
and is closely related to the maximum number of photoelectrons that a pixel can store
which, in turn, is tied to pixel area. For these three cameras
LG G4: Pixel Area = (5.79 mm x 4.01 mm)/16 MP = 1.45 sq. microns
iPhone 6s: Pixel Area = (4.89 x 3.67 mm)/8 = 2.24 sq. microns
Galaxy S6 Edge: Pixel Area = (5.79 mm x 4.01 mm)/16 MP = 1.45 sq. microns
On this basis, the iPhone has the potential for higher dynamic range. And because of
diffraction limits, doesnt really suffer a loss of resolution.
For this particular comparison the system with the f/1.8 lens seems attractive with light
gathering advantages over the competitors, but likely no real difference in resolution,
and possibly less dynamic range. This is consistent with the DXOmark testing for these
phones. A comparison of smartphones with point and shoot or larger format cameras
produces far more dramatic differences
