Roughly the same problems as C++ interop, you can't map common Rust concepts (like error unions, optionals, tagged-union enums, ptr/length-strings, traits) to C APIs without an intermediate shim which does potentially expensive and brittle marshalling, and the C-API is also a 'visibility barrier' for the Rust compiler when it comes to Rust concepts like RAII and ownership tracking.
I think C++ is worse actually due to the lack of move constructors in Rust (move is always memcpy). It means you can't e.g. return std::string by value.
The issues with C FFI are comparatively minor and not at all unique to Rust. Hell, even C++ has those issues when interacting with C APIs. It's not like a std::variant magically becomes a tagged union.
