Working with files between two Linux machines or two Windows machines over the network is pretty easy — in either case, you can share files on one machine and easily access them from the other. In fact, in either case you can mount a remote share and make it appear as part of the local file system, so any application can use the files just as easily as if they were local. This is done via SFTP over SSH (or a number of other methods) on Linux, and via Windows’s native file sharing (SMB) on Windows.
In fact, you can even mount a Windows share on Linux pretty easily using Samba, and use Samba to create shares that the Windows machines can access.
Now, a cool thing about SFTP over SSH is that it typically works even if the machines aren’t on the same LAN. You can access files on a machine across the Internet, and still mount the share so that applications can access the files as if they were local. This doesn’t always work with SMB, as lots of ISPs block the ports required, and even if you can get a connection over the Internet, performance is usually poor.