Everything else being equal, noise, or more accurately signal to noise ratio, is a function of pixel size, not pixel count. The signal is generated by photons hitting the pixel, so the intensity of the signal is given by how many photons hit the pixel during the exposure. Noise is produced by thermal agitation of the atoms in the sensor - vibrations which become more energetic as temperature increases. Thus, at the same temperature and assuming that other variables are also the same, larger pixels result in a better signal to noise ratio, or “less noise”, because you collect more photons for the same amount of thermal agitation. If two sensors are the same size, then the one with less pixels would, everything else being equal, have less “noise”. The ultimate example of this is the Sony A7S, full frame with 12 Mpixels. I have pictures at ISO 10,000 with very little noise, and ISO 3200 is as routine with it as ISO 200 was on film.
But the “everything else” is important here, and when you see these comparisons you need to ask how they were made. For instance, noise (thermal agitation) varies exponentially with temperature, so if one sensor is warmer, because it has been recording for a longer time or because ambient temperature is higher than when the other was tested, this may negate the advantage of size. This is why sensors used in astrophotography are cooled (e.g., with liquid nitrogen). Also important is exposure length - the longer you take to record the same number of photons, the more noise there will be. That is why when you do long exposures you need to balance exposure length with ISO, as you decrease ISO you increase exposure length and thus noise, and there is an optimum compromise that you have to determine empirically. And of course there is sensor technology and construction, and not all sensors are equal in this respect. As Nathan notes, Sony sensors and some other sensors also made by Sony (read those in Nikon cameras) are particularly resilient to noise, for reasons that are almost certainly trade secrets. Other Sony sensors (e.g., those in Olympus cameras) are not nearly as good, even accounting for the fact that pixels in 4/3 sensors are very small.
Bottom line, and as with everything else, don’t believe anything you read or hear unless you get full disclosure of how measurements were made. Even with DXOMark, who are very rigorous and open in their testing procedures, I have found that my experience does not always agree with theirs. For instance, according to their measurements the Sony A7S has less dynamic range than the A7R, well outside the margin of error. My own experience with both cameras is the opposite, I find that the A7S gives me more dynamic range than the A7R, but this may be affected by the way I expose as opposed to the way the tests were carried out.
I hope this helps ….