Which rule you use depends on what information you have been given.  For  example, if you have been given the length of three sides of a triangle and are trying to find the size of an angle, you would use the cosine rule - in this case the sine rule wont help you.
In some cases, you can use either rule.  In general, the sine rule is easier to use, but since sin(A) = sin (180-A),  sometimes the sine rule will yield an ambiguous answer.