If you have 12,000,000 pixels and you put those pixels on a 36 mm x 24 mm image sensor, each of those 12,000,000 pixels are bigger than each of the 12,000,000 pixels on a 23.6 x 15.8mm (1.5 crop) image sensor.
The bigger the pixels are, the more light (bigger signal) they can gather. The more light (bigger signal) they can gather, the less image noise there is.
Be sure and take those Physics classes.
That would suggest that a camera with less megapixels would always be preferred. Obviously the pixels will be smaller as the number of MPs increases given constant sensor size (be it crop or full frame). But I'm guessing that as the MPs increase, camera manufacturers figure out ways to capture more and better quality light in sensors with smaller pixels. Correct?
Yes, that's correct. The comparison made assumes identical technological capability in the production of each sensor. As the whole industry moves forward, every sensor has better noise/dynamic range than the previous generation. As well resolution goes up across the board. The point is that given a certain level of available engineering, a full frame sensor will always perform better at the same resolution. When you start comparing between generations the lines get fuzzy. There are new crop sensors that have higher resolution AND better ISO performance than certain old full frame sensors.
Now hold yer horses!
While everything you're saying is true, there is one fact that I think people miss out on.
Say you have two hypothetical sensors with identical Signal to Noise ratio, one is a lower resolution APS-C and the other is an slightly higher resolution 35mm, at around ISO 6400 these two sensors both start chugging out appreciable noise, and because the light sensor surface of both are about the same they both produce, EXACTLY the same amount of noise.
Now. Step into your time machine and go back to 1995 for a second. Before you there is a box of 8x10" TMAX 400 and a roll of 35mm TMAX 400. The client needs something with no visible grain. Which camera are you going to pick up, the Linhoff or the Nikon?
Funny though - both films are TMAX 400. Shouldn't they produce the same amount of grain? Of course they do, and as every photographer knows that grain doesn't need to be enlarged as much (if at all) with the 8x10 film. And that is why the 8x10 will seem smoother, when in fact it's really not.
Now. Back to the future and the two impossibly similar digital cameras. The same principle applies here. While the smaller sensor produces as much noise as the larger one in this case, the higher resolution APS-C will require more reduction in size to meet a specific end print size, as a result the noise - while being there, just like with the 8x10 film - becomes less noticeable.
This is exactly what I was thinking when I was looking at the NEX-5n and the NEX-7. While the NEX 5n does *slightly* better than the 7 due to it's lower resolution, the NEX-7 produces significantly larger files. So while at the maximum possible print size at any given dpi I might see slightly more noise on the 7, however due to the amount of reduction in any specific print size, I'd actually see less or similar noise. Especially considering how similar the 5n and 7 perform.
That of course is assuming that we all know how to use the light meter every single time and that if, in the weird instance we do screw up (which would never be out fault) we don't reach for the "exposure" slider in the RAW processor. Who would ever do such a thing? Obviously, lower noise also means better integrity and more flexible files. But that's another barrel of monkeys.