In writing Win32 C/C++ code, is there any advantage (e.g. performance?) in using Windows-specific functions like lstrcpyn or CopyMemory instead of
It depends on the function and your requirements.
For things like memcpy, there isn't any point whatsoever to choosing the Windows-specific versions. Stick with standard C to keep it simple and portable.
For other things like mbstowcs, you might need to use things like MultiByteToWideChar instead -- depending on what functionality you need.
Personally I go for the C versions if possible, and only go for Win32 versions afterwards -- because there's really no reason to write Windows-specific code when it could be written portably.