C++ has more potential (indeed thanks to metaprogramming), but the average idiomatic C program is often faster. C++ tends to do a lot of implicit allocation, or initialize values even if not necessary. Also, smart pointers are not free (at least shared_ptr and weak_ptr are not).
If you have a good understanding of how C++ works, eschew convenient but costly C++ features, and care to optimize. You may get better performance than C. I guess that's part of the reason why most game engines are made in C++.
Important to note though that you will only get fast if you turn on compiler optimization, which actually is a problem as debug builds may end up unusably slow.
This has not been true for a long time. Modern C++ consistently outperforms C in practice, mostly due to its extensive metaprogramming facilities.