This will probably not be a popular answer, but I think what sets C++ apart are its compile-time capabilities, e.g. templates and #define. You can do all sorts of text manipulation on your program using these features, much of which has been abandoned in later languages in the name of simplicity. To me that's way more important than any low-level bit fiddling that's supposedly easier or faster in C++.
C#, for instance, doesn't have a real macro facility. You can't #include another file directly into the source, or use #define to manipulate the program as text. Think about any time you had to mechanically type repetitive code and you knew there was a better way. You may even have written a program to generate code for you. Well, the C++ preprocessor automates all of these things.
The "generics" facility in C# is similarly limited compared to C++ templates. C++ lets you apply the dot operator to a template type T blindly, calling (for example) methods that may not exist, and checks-for-correctness are only applied once the template is actually applied to a specific class. When that happens, if all the assumptions you made about T actually hold, then your code will compile. C# doesn't allow this... type "T" basically has to be dealt with as an Object, i.e. using only the lowest common denominator of operations available to everything (assignment, GetHashCode(), Equals()).
C# has done away with the preprocessor, and real generics, in the name of simplicity. Unfortunately, when I use C#, I find myself reaching for substitutes for these C++ constructs, which are inevitably more bloated and layered than the C++ approach. For example, I have seen programmers work around the absence of #include in several bloated ways: dynamically linking to external assemblies, re-defining constants in several locations (one file per project) or selecting constants from a database, etc.
As Ms. Crabapple from The Simpson's once said, this is "pretty lame, Milhouse."
In terms of Computer Science, these compile-time features of C++ enable things like call-by-name parameter passing, which is known to be more powerful than call-by-value and call-by-reference.
Again, this is perhaps not the popular answer- any introductory C++ text will warn you off of #define, for example. But having worked with a wide variety of languages over many years, and having given consideration to the theory behind all of this, I think that many people are giving bad advice. This seems especially to be the case in the diluted sub-field known as "IT."