This should be highschool level deduction.
The basics
In short:
Assuming equivalent sensor technology where read noise or thermal noise doesn’t dominate:
1. Low light performance (low noise in low light photos) is dependent on absolute aperture size
2. Dynamic range (avoiding saturation in bright areas while still lighting dark areas) is dependent on pixel size
In slightly more length:
1. You catch more photons from the same target with a bigger aperture. With more photons, there is less randomness.
2. A small pixel saturates with less photons than a large one. If you have low dynamic range, you either blow highlights or lower the exposure so that highlights are not blown, but then you get more noise in the shadows.
What this does not mean
A larger sensor by itself does NOT improve low light capability. The lens with a certain aperture diameter (mm) can only catch so many photons*
You have to enlarge the optics to get a good low light performance, not the sensor. You can keep a smaller sensor and just enlarge the optics to reach the same result as with big optics and big sensor.
What you are being sold
Let’s see what cameras are sold with:
A. Zoom factor. More of this usually includes the lens design tradeoff of making the aperture much smaller so it hurts low light performance.
B. Megapixels. More of them means the pixels are smaller and that lowers dynamic range.
As a result we get cameras that have blown highlights and/or noisy dark areas outdoors (too small pixels) at best, and completely noisy images everywhere when used inside (too small aperture).
The fix would be:
1. Enlargen the aperture. So throw away the zoom lenses and go with well designed primes. Immediate improvement in low light performance.
2. Lessen the amount of megapixels. People have to resize down for web anyway. 2 megapixels could be good. 1000×2000 is bigger than almost any web graphics. One could go down to half a megapixel, 500×1000.
The results could be phenomenal. The photos could be indistinguishable from full frame DSLR photos at the same half megapixel resolution and modest focal lengths! Except maybe for background defocus. Even a 0.7 megapixel image won’t fit here, you have to click it:
A 0.7 megapixel image by Jean-Marie Huet. WordPress isn’t very good with images I’m afraid so you have to click the image. It’s shot with a 5 D mark II.
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