The C++ API is newer and offers the benefits like better type-safety and automatic memory management (due to use of C++ containers). It is also part of a general trend that more and more software is C++ (as are the developers).
For interfacing to Fortran I was surprised by how much easier it was to write the C MEX function. You just need to follow the steps
- unpack contents of
prhsinto corresponding C types - prepare any output buffers to pass to Fortran
- call your Fortran routine
If you avoid doing any other operations in the C MEX function you should remain pretty safe.