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Both D3100 AND D3200 have similar, almost identical, sensors. Which is going to give the best image quality if I set them both to, for example, 12MP? I also also placed the pixel sizes below.
D3100 - APS-C 23.1x15.4mm 25.1 µm²
D3200 - APS-C 23.2x15.4mm 14.8 µm²
With two sensors the same size, whether the one with fewer, larger pixels or the one with more, smaller pixels is best for you depends in large part upon what conditions you are most likely to shoot in and how you want to use the images you create with the camera. It may also depend to one degree or another on how much better the next generation of technology used in the D3200 compares to the slightly older technology of the D3100.
If your primary concern is low light performance then in general fewer, larger pixels will outperform more, smaller pixels on sensors of the same size. This is due to the amount of space lost between each pixel (unless a sensor is 'gapless'), and also due to the three-dimensional shape of the pixel wells that mean the narrower the well, the fewer percentage of photons that strike the surface of the sensor make it to the bottom of each pixel well and get recorded by the sensor. Please see Why and how do "bigger pixels" make a better picture? for more.
If your primary concern is resolution that will enable you to produce very large prints or to crop one particular section of an image for enlargement, then the sensor with more pixels will give you more working room in that respect.
In the particular case of the D3100 vs. the D3200, here is a side-by-side comparison of the two at DxO Mark. To see the results from a particular test click 'Measurements' and then the tab for 'Sensitivity', 'SNR 18%', 'Dynamic Range', etc.
The most significant difference I see: The D3200 has almost two stops better Dynamic Range (DR) at ISO 100, about one stop more at ISO 200 and a half stop more DR at ISO 400. Part of the DR advantage is because the actual sensitivity of the D3200 is about 1/3 stop lower at each ISO setting than the D3100. With both cameras set to ISO 200, for instance, the D3100 performs at ISO 182, while the D3200 performs at ISO 140. (These variations are fairly typical of most DSLRs.) The D3200 shows a similar advantage in terms of Color sensitivity.
Please note that all DxO scores are based on images resized to 8MP, so resolution is not reflected in either the overall DxO score or any of the use case scores (Portrait/Landscape/Sports-Action). Based on that, I'd say the D3200 wins, especially with high dynamic range scenes or scenes with a lot of fine tonal gradations within the same colors.
It depends on how the image processing works and what lenses you have on it. Most likely the d3200 will look either the same or better since under certain conditions it will have more information to start with. If the lens has a resolution higher than the native resolution of the sensor and you are not diffraction limited (shooting relatively open aperture) then there will be more detail to be used when down-sampling which will produce a greater level of noise reduction due to averaging over more samples.
Under other conditions however, the original images may have effectively very near the same effective resolution in which case the images would be very near the same. For practical purposes, all other things being equal, the higher the MP the better, but the trick is to make sure all other things are equal because the higher the number of megapixels gets, the smaller difference it makes. It is still an improvement, but other factors become much more significant.
