Is the image being reduced in colour? FLI and GIF have a 256 colour limit. MNG probably does to.
If you want whatever you literally make to be the same, make sure it stays within the limits of the format you save it to. If that doesn't work then the only other possibility is there is something wrong with the gimp's saving ability in that format. Check the image settings in the gimp to see what it says about RGB/Greyscale and so forth. See what you have selected.
Then comes the next thing, it depends a little bit on what your trying to do. There isn't a good standard of animation in my opinion in image formats alone. If you want good higher quality then consider spliting up your animation in a series of images.
I have no idea what your trying to do, but I will take couple of shots in the dark. If your doing web work, you may want to know I've seen javascript on web pages that flip between a series of images for animation, so that's an option. If your drawing 2d sprites, then just remember that older games have a 256 colour limit and that's one reason for the 256 limit in the old format.