There are almost no scenarios where it is a good idea to use the Fit To Composition option because unless the original picture aspect ratio exactly matches the frame aspect ratio you will distort your image. I usually see this question when folks are mixing non square pixel footage with square pixel footage. This can get very confusing. As long as the footage is properly interpreted you should be using the Transform>Fit to Width or Fit to Height options from the Transform Menu or the keyboard shortcuts. You just live with the black bars if the footage does not fit the frame or you crop.
If you are dealing with non square footage like DV-Widescreen or DVCPRO HD and are having problems with interpretation or you are working in a NON SQUARE Pixel or Custom Composition size and are having problems let us know. With some specifics we can help you out. Unless you are expert in formats and non square pixels your main comps should not show Custom or anything other than Square Pixels in the Composition Settings.
Make one composition in which you fit your content to the width.
Put that comp in a new comp where you scale it to fit the height.
In my case I needed to do this to position and scale a folder of pngs to a square.
Hope this helps!