Varies. Sometimes there is a big difference, sometimes none. If graphics are simple (your sig for eg), you probably won't gain anything with brute.
FYI, 8bit is a good bit smaller than 24bit. C2 can do that, but I like this tool better:
PNGoo: http://pngquant.org/
Free batch converter, using same algo as kraken.io/TINYpng.