The differing behavior between the disks is due to the difference in the default umask between the two filesystems (NTFS and ExFAT) on Linux. For NTFS-3G, the default umask is 0000; for ExFAT it’s the umask of the current process (likely 0022).
These are mask values and are applied at file or directory creation time. For example, for a directory which would be created with 0777 permissions (read, write, execute for everyone) on a file system with a umask of 0022, the effective permissions would be 0755 (read, write, execute for the owner, read and execute for group members and others).
This corresponds with what you’re seeing above; your NTFS disks are mounted with effective permissions of 0777 (0777 - 0000) while your ExFAT disk is mounted with effective permissions of 0755 (0777 - 0022).
The easiest way to “fix” this if you want the behavior of your ExFAT disk to match that of the NTFS disks is to mount it with a umask of 0000. To do this, you’d add the umask option to your mount options. Something like:
UUID=619D-E596 /disks/hddrive3 auto nosuid,nodev,nofail,umask=0000,x-gvfs-show 0 0
A more nuanced approach than making the disk world-writeable would be to give ownership of the mount to a specific user and group, and then use that user and group to manage the content of the disk. You can set ownership with the uid and gid mount options. In combination with the umask option:
UUID=619D-E596 /disks/hddrive3 auto nosuid,nodev,nofail,uid=your_user,gid=your_user,umask=0002,x-gvfs-show 0 0
This would give ownership to your user and group and allow that user and group read, write, and execute permissions. Others could only read/execute.
But, again, the easy solution would be the first one and just make it world-writeable; your NTFS disks already are and it would certainly ease management from a Windows system.
