Hard to tell without seeing the colormap of the indexed file, but maybe JASC actually generates an optimized palette rather than using a standard? I would say that image No. 1 is better in skin-colors. Does the colormap of Nr.1 have any unused colors - except index 254 and 255 (or 0 and 1 in JASC)?
In GIMP the palettes are stored in a separate folder, but they can be imported from images and files anywhere on the disk (as long as they have a correct file extension, of course) . I would guess there are similar possibilities in other graphics software, but I don't know in detail how other programs handles palettes, I'm afraid. Are you using Paintshop?
Anyways, If you figure out how to import palettes and want me to make a custom .pal for testing later, just shout.