Using Photoshop CS4 'Save for Web & Devices' -- I can tell with the Color Table how many colors are in use in the PNG-8, but am not sure how much downsampling to 256-colors is reducing the color depth of my image.
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You can measure it with ImageMagick:
or with DSSIM:
MSE is mean square error and DSSIM is structural (dis)similarity metric. The latter is a bit more closely aligned with human perception of image degradation, but both are just estimates.
Also when you convert images to 256-colors with latest version of pngquant it will show MSE in verbose mode: