a. JPEGs are better for Photographs and images 
  with colors blending into other colors. They also permit a greater degree of 
  compression than GIFs and can be smaller. 
 
 
  b. GIFs 
  are better for images with flat fields of color.
  GIFs can have transparency (like the ones below) and JPEGs can't.
  GIFs can be animated. 
  
  
But, they do this thing called dithering if colors are not in the GIF color palette. Dithering is when the computer approximates colors for you, often a bad thing.
 
 
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