C++ is like C with extra features, but you don't need to use them.

If you want control over your memory, you can do pointers the C way, but you still have features like templates, namespaces, etc... Another advantage of C++ is that it can go both high and low level within the same language.

Disadvantage of C++ is mostly related to portability and interop. Things like name mangling, constructors, etc... can be a problem. Also, C++ officially doesn't support some C features like "restrict". In practice, you often can use them, but it is nonstandard. Probably not a concern for HPC.