Applications and differences for Jaccard similarity and Cosine Similarity
The answer from saq7 is wrong, as well as not answering the question.

∥A∥ means the $L2$ norm of $A$, i.e. the length of the vector in Euclidean
space, not the dimensionality of the vector $A$.  In other words, you
don't count the 0 bits, you add up only the 1 bits and take the square root.

Sorry I don't have a real answer as to when you should use which metric,
but I can't let the incorrect answer go unchallenged.