Well, It's not 100% correct but generally yes. because it's all about the size of the individual pixel.
e.g. if it's raining and there is two guys standing in the rain. the first one is holding a glass and the second is holding a big bucket.
after 5 minutes you'll find that the bucket has collected much more water than the glass.
the same principle works for pixels. a big pixel collects more light than the small pixel. in this case more light is considered more information and more information means that the in-camera processor won't need to do too much amplification in order to produce the final image. and the less amplification the less noise you get in the final image.
Another thing is dynamic range.
Dynamic range is defined as "the ratio between the smallest and largest possible values of a changeable quantity". so in case of an empty glass and a full glass, there is a lower ratio between them if compared with the ratio between an empty bucket and a full bucket.
So a bigger pixel gives you greater dynamic range.
Now, this is theoretically correct to a point. which is that the sensor technology does not change.
So, in reality another variables change in the equation. e.g. sensor technology, gapes between each individual pixel, in-camera processing technology.
so , if we take these cameras as an example: the canon 5d and the canon 5d mark 2.
the first has a resolution of 12 million pixels.
the second has a resolution of 21 million pixels.
and both sensors are of the same size, which means that the individual pixel is smaller in the high pixel-dense sensor.
At first, we think that the first is going to have better image quality. in terms of image noise at least. but then we find that this is not the case.
Check this and compare for yourself:
http://www.cameralabs.com/reviews/Canon ... oise.shtml
For my unexperienced eyes, I see that the 5d mark 2 has less visible noise.(at least when we exclude things like sharpness)
Some of the reasons for the mark 2 having comparable (if not better) noise performance are the improved sensor architecture, the micro lenses improved design, better on-chip(sensor) noise reduction and better processing and noise reduction algorithms.
But, most of the time this is not the case. We are taking about two professional cameras here (some might argue with that).
So in the case of two compact cameras there really will not be a huge breakthrough when it comes to the sensor design and in-camera processing technology. So the rule of "less pixels equals less noise" applies perfectly.
In conclusion, unless there is a major improvement in other things like mentioned above, the answer is yes. the less the number of pixels the better image quality you get(in terms of noise performance and dynamic range).
Hope that was helpful.
forgive me if I sounded like a huge nerd