The amount of size that can be reduced with the ZIP format depends on how compressed the files already are.
You're unlikely to get any significant reduction with files that are already highly compressed. For instance, if you zip a JPEG image file, an MP3 audio, or an MPEG video file, you won't save much space. However, if you're trying to compress a WAV file on Mac, you may find about 50% size reduction.
WinRAR uses a completely different compression algorithm than Archive Utility on your Mac and apparently, it does a better job compressing your files. If I were in your shoes, I'd try a different file compressor to zip files on your Mac and see if it makes a difference.
iBoysoft MagicMenu may be a good fit. It works similarly to the built-in compression but allows you to select different compression levels and protect the compressed file with a password. You can get it from the button below and choose the highest compression level to ensure maximum size reduction.
