If you need restart, rsync is probably the way to go. One of the fastest ways over a network, I've found is with "Samba" -- but to get excellent performance it usually needs to be tuned for the environment. But what I mean by "fast" is on a 1Gbit ethernet,
125MB/s writes and 119MB/s reads. The 125MB/s writes are as fast as you are going to get unless your payload is able to be compressed -- i.e. a 1TB text file would likely compress to 1/10th the size.
Note... problem w/rsync, "direct" is that it generally uses some other protocol (rsh/ssh) to do do the transfer -- if you use rsync over 'ssh' you will incur an encryption cost, which on a good machine adds a ceiling of 140-160MB/s. That will usually drive up latency on a network connection and slow down overall transfer be 50% or more.
So the fastest way depends on what type of network you have in place between the two machines. Slow-ish Internet speeds (i.e. .5-10MB/s), or a local area network (w/1Gb or perhaps even
If transfer speed is most important and more so than overall
speed, i'd "prep" the file for transfer by running it through
a good compressor (like xz or 7z) -- BUT that will take a large chunk of time by itself (so overall time is likely to be larger). But if actual transfer speed is more important, then compression becomes a good way to cut down on that.
It really depends on where your priorities are and how much time you want to spend optimizing the transfer speed. Overall, though, I think sirlancelot gave the right answer, just that there can be many mitigating factors depending on your priorities.