I was talking to someone the other day. He said that given two Turing Complete programming languages, A and B, if you can write a program in A, you can write a similar program in B. Is that true? I suspect not.
I never took a class on computability theory, but I suspect it only works for a limited subset of programs--ones that only require the features provided by a Turing machine. Let me provide a counterexample. Let's suppose that language A has networking APIs and language B doesn't. Nor does language B have any way to access networking APIs. It's entirely possible for language B to be Turing Complete without actually providing such APIs. In such a case, you can write a program in language A that you can't write in language B.
Of course, I could be completely wrong because I don't even understand the definitions fully. Like I said, I've never studied computability theory.