option A: use NAS if the volume will be accessed by both systems in long run
option B: plug the hard drive to either one system (depends on which needs faster access), use native file system of the host system, and share the volume through network
exFAT is natively supported by both systems and without 4GB limit, but not recommended for long term use and for large volume. It does not support journaling means it is easy to corrupt. Permission support is also a nightmare.