- What is the fastest way to do it? FTP? rsync/rcp/scp? Something else?
- Is there something to be tuned for this amount of traffic?
Frankly, your question is a bit vague asked, so I try to need to understand some things to give an usable answer:
You do have two servers, let's call them A and B.
A is producing X B/s data. A's data shall be transferred to B.
The bandwidth of the net you're using is N B/s, and apparently X > N, otherwise you wouldn't have asked.
If not, measure your data throughput N first, and get exact numbers on X. If those don't fit it's useless to talk about the protocol at all. The net's bandwidth is independently from the protocol you're using, ftp, scp, rsync... of course some are faster than others, while none increases the bandwidth.
So, by principle you have two options, only:
1. increase N
2. reduce X
For 1 - see how to get more bandwidth, you have two options: Ask or find a provider for a faster line. If there is no line available fast enough, your only options left then are: Build a line yourself. Which, of course, can be a bit problematic, if you have more to span than some few hundred meters on your own property, and money matters.
Or you can do what
covacat said: Do copies of the data to storages (tapes, HDDs, SSDs,...) and ship those with some parcel service, or drive them yourself over to B. You can get amazing bandwidths this way: Just imagine you put thirty 10TB drives into a parcel, and calculate the B/s you get when this package needs 48h for delivery.
Or 2, you need reduce the amount of data that needs to be transferred. Remove all data, which doesn't need to be transferred, or at least at the same time, and select only data really needed.
As you say the data is mostly videofiles. So there is no really more you can compress anymore.
So check if there is a file format your raw videos could be saved with better compression. And see if you can reduce the video files raw data: lower resolution, FPS, colors,...
For 2 you said, everything could be done was done.
So 1 is left: get a line fast enough, or ship storages.