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Great question!
The short answer is: You can't reduce image noise either way, so don't sweat it. Most of the noise you see in images from point-and-shoot cameras is something called "photon noise", which is a function of the total amount of light captured. Pixel size has no effect on this.
The long answer: A camera with more small pixels will always have less total noise than the same camera with fewer big ones because of read noise. Like photon noise, read noise is independent of pixel size. A tiny pixel from a Canon PowerShot has just as much as a huge pixel from an EOS 5D (and often, less).
Here's where it gets a little confusing: Let's say you have two hypothetical 1/2.5" cameras with different megapixel counts. If both the large and small pixels have equal read noise, and you resize the big picture made with small pixels to the same size as the little one made with big pixels, the signal from each small pixel adds linearly, but the read noise from each small pixel only adds in quadrature. What you get is an image with just as much photon noise (since it isn't really noise at all, but part of the signal), *less* read noise, and therefore less *total* noise.
There's really no benefit to using big pixels. Anything one big pixel can do, four smaller ones with an equal combined area can do just as well, and often do better. If you're stuck at one sensor size, get as many as you can.
Screwdriver:
>> ... a small sensor with loads of pixels will have more
>> noise and not perform as well as a larger sensor with
>> the same amount of pixels
Right. Because it's a *smaller sensor*, not because it has smaller pixels.
>> or a same sized sensor with fewer pixels in low light.
Nonsense.
>> Funnily enough it came up in our club just last night...
You ran a test by comparing JPEG conversions from three different cameras with unequal sensor sizes, with unequal processing, with unequal technology, and with unequal expectations, then attributed the inequality to the pixel pitch?
The "smaller pixels = more image noise" argument has no basis in reality. People have become so comfortable with the half-baked logic behind this myth that they speak as if it is a basic truth, but no one can provide any evidence to support it. Misleading statements like yours do not help.