My understanding is that most implementations of new call malloc under the hood (this may or may not be outdated at this point, I haven't kept up with C++ implementation) and both of these systems introduce a layer of record keeping, so if you're in an extremely memory constrained environment, you may want to use malloc directly.
If you want your code to be noexcept, you need to call malloc and handle the case where it returns null as new can throw (this is UB in theory, but in practice I'm pretty sure everything just aborts) to strip out all the stack-unwinding code.
If you want to avoid the constructor call (for whatever reason).
We are talking about the question if C is a subset of C++.
`new` certainly isn't a part of C, so also not an element of the intersection of C and C++.
Idiomatic C code doesn't explicitly cast the return value of malloc
foo *bar = malloc(sizeof *bar);
C++ did AFAIK never (certainly not with C++98, the question is if it had been allowed sometime before the standardization, but I think it never did) allow this, so you always had to do
foo *bar = (foo *)malloc(sizeof *bar);
Therefore, C is not a subset of C++. But a (non-empty ;) intersection of C and C++ exists.