Is it better to use std::memcpy() or std::copy() in terms to performance?

Is it better to use memcpy as shown below or is it better to use std::copy() in terms to performance? Why?

char *bits = NULL;
...

bits = new (std::nothrow) char[((int *) copyMe->bits)[0]];
if (bits == NULL)
{
    cout << "ERROR Not enough memory.\n";
    exit(1);
}

memcpy (bits, copyMe->bits, ((int *) copyMe->bits)[0]);