Following on from my Project 2013 thread and a few similar posts, we have mentioned the use of polarizers and whether they were worth using.
For general use, I have found that I can mostly achieve the same results, or better, from different shooting and/or processing options.
But I intended to do some more experimentations.
Looking at the final edits, which is what mostly matters, I found virtually no difference with regard to saturation, brightness, contrast, etc. But there does appear to be a considerable difference concerning the amount of image noise.
Some close crops to show the difference. An overcast day and I was shooting at 90 degrees to the light.
The difference will be most noticeable at full screen size.
There was also quite a bit of variation in the available shutter speeds, as you would expect, which ranged between 1/100 with polarizer to 1/500 without for the same scene.
I just used some slight noise reduction while converting the Raw files; not specialised software.