GIF

GIF will produce a higher quality image for such things as line drawings, cartoons, icons with only a few colors and images with only a few unique colors. Quite often it will compress them better than JPEG, as JPEG will lose quality on images with large areas of pixels that are all exactly the same color .

As an example, consider the two graphics to the right both showing a large expanse of white. Note that the quality of the jpg appears splotched, the background appearing almost as if it were a lined sheet of paper.

Here we have 3 banners, of almost equal quality. The first is an 8 bit gif, at 14kb, the second is a 4bit gif, at 8kb, and the bottom one is a 24bit jpg. totaling 11kb. The quality of the jpg is not quite as good as that of the gifs. Thus, we see that for line art, the gif format can produce a smaller file, with better quality than a jpg.

Sources:

Jasc.Inc
Bandwidth Conservation Society
The Ohio State University Dept. of Computer and Information ScienceJPEG Image Compression FAQ, part 1/2
Preparing Graphics For The Web
Which format is better for WWW image purposes, JPEG or GIF?