Which filesystem is compatible with GNU/Linux and Mac OS? I want to be able to read/write from both GNU/Linux and Mac OS. For example I want to copy a file to my external hard-drive from GNU/Linux and then copy it from the external hard-drive to Mac OS.
I know FAT works but I want it to support files bigger than 4GB.
You probably want the ExFAT filesystem. Works on OSX, Linux and Windows. Supports large volume and file sizes. Here is some information How to enable exFAT in Ubuntu on exFAT support in Linux.
The default OS X filesystem, HFS+, works in Linux. But first, see: