Passing comparison functor by reference or value

I noticed that some std classes/functions take function parameter by value and some by reference.

For instance, std::sort takes comparison function by value:

template<... class Compare>
void sort( ..., Compare comp )

And std::set constructor takes comparison function by reference:

template<... class Compare>
class set
{
    explicit set( const Compare& comp, ... )
    ...
}

Why this difference, and in what cases is one or the other method preferred?