That may be true, but we have been very careful with colour count and such, especially with sprites it tends to be better that the information is lost because with 1000+ sprites in our game, we don't tend to care as much that the program may have a sprite where two different colours have been grouped together because they are very close since on a larger scale it compromises the filesize of all our sprites. I also would not care about hidden image tags and such.
Looking at the sprites, there is no actual visible difference between them, so that is what matters most along with filesize
edit: when I save as gif on paint.net it gives me dithering and transparency threshold sliders. On photoshop it allows me to choose the palette of colours to be used, the matte, forced colours and I check whether or not there is transparency
oh and, since I am working with sprites, I do not bother with dithering and such, so the settings for those on paint.net and photoshop are ignored. On photoshop the palette is always exact