There's a considerable difference when you have templates and start taking base class(es) as template parameter(s):
struct None {};
template<typename... Interfaces>
struct B : public Interfaces
{
    void hello() { ... }
};
struct A {
    virtual void hello() = 0;
};
template<typename... Interfaces>
void t_hello(const B<Interfaces...>& b) // different code generated for each set of interfaces (a vtable-based clever compiler might reduce this to 2); both t_hello and b.hello() might be inlined properly
{
    b.hello();   // indirect, non-virtual call
}
void hello(const A& a)
{
    a.hello();   // Indirect virtual call, inlining is impossible in general
}
int main()
{
    B<None>  b;         // Ok, no vtable generated, empty base class optimization works, sizeof(b) == 1 usually
    B<None>* pb = &b;
    B<None>& rb = b;
    b.hello();          // direct call
    pb->hello();        // pb-relative non-virtual call (1 redirection)
    rb->hello();        // non-virtual call (1 redirection unless optimized out)
    t_hello(b);         // works as expected, one redirection
    // hello(b);        // compile-time error
    B<A>     ba;        // Ok, vtable generated, sizeof(b) >= sizeof(void*)
    B<None>* pba = &ba;
    B<None>& rba = ba;
    ba.hello();         // still can be a direct call, exact type of ba is deducible
    pba->hello();       // pba-relative virtual call (usually 3 redirections)
    rba->hello();       // rba-relative virtual call (usually 3 redirections unless optimized out to 2)
    //t_hello(b);       // compile-time error (unless you add support for const A& in t_hello as well)
    hello(ba);
}
The fun part of it is that you can now define interface and non-interface functions later to defining classes. That is useful for interworking interfaces between libraries (don't rely on this as a standard design process of a single library). It costs you nothing to allow this for all of your classes - you might even typedef B to something if you'd like.
Note that, if you do this, you might want to declare copy / move constructors as templates, too: allowing to construct from different interfaces allows you to 'cast' between different B<> types.
It's questionable whether you should add support for const A& in t_hello(). The usual reason for this rewrite is to move away from inheritance-based specialization to template-based one, mostly for performance reasons. If you continue to support the old interface, you can hardly detect (or deter from) old usage.