When should you use direct initialization and when copy initialization?

The actual names of the things you describe is not implicit and explicit assignment but :

• Copy-initialization : T x = a;
• Direct-initialization : T x(a);

They are not equivalent, most notably in contexts where a conversion is required, for example when T is of class type and a is of a different type (see Alf comment for examples of contexts which don’t even involve conversion). Consider the following code :

class Test
{
public:
    explicit Test(int i) { /* ... */ }
};

int main()
{
    Test t(0);  // OK : calls Test::Test(int)
    Test u = 0; // KO : constructor is marked explicit
}

To paraphrase the standard (8.5/14) :

• For direct-initialization and copy-initialization where the source type is the same as, or a derived class of, the class of destination, constructors are considered
• For other copy-initialization cases, like the second line of main in my example, user-defined conversion sequence are considered. As the use of the Test constructor for implicit conversion was disallowed by the explicit keyword, the second line fails to compile.