Can you elaborate on this one? Noise is noise, no matter which source it comes from (sky flux poisson process or read noise or thermal noise), it may have different statistical characteristics, but in general it will be random unwanted addition to signal.
My view on things including original question is as follows:
Prefer mosaic + software binning (of stacked and stitched mosaic) over focal reducer (at least over any reducer that has not been specially designed for particular scope and of highest quality).
Pros of mosaic + software binning:
Smaller FOV to work with - less off axis aberrations of any kind (coma, astigmatism, field curvature) which are usually amplified by focal reducer.
Making mosaic in general does not require much more time to achieve target SNR (not really true due to read noise, but close enough). For example: you consider to take 16 subs over target area. In case of mosaic (2x2) you would use 4 subs for each mosaic segment. 16 subs would give you x4 SNR after stacking, while for other case: 4 subs per segment give you x2 SNR reduction for segment, and then you bin 4 segments (mathematically it is equivalent of stacking 4 subs) - x2 SNR increase again - 2x2 = x4 SNR, same as in first case. SNR has quadratic dependence, but so does area.