Modern computer architecture is indeed modeled after the
Von Neumann architecture. However, more generally, they are a hardware implementation of what's called a
Turing machine. In essence, Turing discovered his machine could compute the result of all "computable" problems. An alternative line of theory is the
lambda calculus, which was found to be equivalent to Turing's model of computation, but free of side-effects. Certainly this is an interesting (if abstract) study, but IMO is not a topic generally for discussion on this forum, which is more in line with practical programming. Which brings me to my point. Studying the background of theoretical computation is interesting, but IMO will do little do increase your practical programming skills. You need to decide which is of more value to you: talking theory with mathematicians, or with real-world programmers?
Also, to answer the question posed in your topic question: C and C++, and all other so-called
Turing complete languages, are equivalent in the sense that they can compute answers to all "computable" problems. However, beware the
Turing tarpit.