I'd use rsync.

Do you have easy physical access to the other machine? If so, the absolute easiest way is to plug a removable device of some sort into your machine (your phone will likely work if you don't have any USB drives handy), copy the data over, and then plug the device into the other machine and move the data from the device.

You need to be more specific. Are you asking about link method, or software tool?

Take the drive out and put it in the other computer.

Or be patient and let it go overnight.

I've used various tools for that, they kinda all work. A Windows network share, or just type in "ssh://user@IP" into the Nautilus file explorer and drag and drop. You can bookmark the address so you don't need to type it in the next time. If you do it on a regular basis you can alternatively configure a NFS share and the other computer's filesystem will look just like any other directory and you can copy files as usual. If you want to transfer terabytes of files or they're millions of small files and you want nice error messages and continuation if something goes wrong, it will be worth doing it with rsync. But you need to look up the parameters (or use a helper), there's a bunch or arguments needed to make it do the right thing.

In any case it should transfer roughly 4GB per minute if you have a Gigabit network. I'd say ~250GB per hour. Maybe a bit more or less. But all methods will do it at the same speed unless you tweak it, change compression on transfer...

Good ol' rclone

On Ubuntu, just install gnome-user-share on one machine and now you have a Sharing>File Sharing section in Settings. It's point and click.

Everything on the NAS.

Then network shares are the answer.

I would make sure both sides are using ZFS then transfer ZFS send/receive snapshot diffs.

The neat thing about ZFS is by its design it already has the known differences between source and destination, so calculating the diff is trivial. It can also stream blocks as fast as your drives can read them since it's not handling individual files but block streams.

http://pairdrop.net/

Depends on how large though, or how many files. But I think this would work for <80 gig stuff reliably.

You might have to zip it up beforehand if it's many small files.

The best way? External drive. I mean, if they're on the same local network presumably you physically have access to both machines.