You can use SSH to pipe data between two boards. If you like, you can setup shared SSH keys, so SSH will not ask for passwords (this gives some instructions SSH/OpenSSH/Keys - Community Help Wiki)
For example on the first board (that collects the data) you can run something like:
ssh <IP_of_the_second_board> tail -f /my/remote/data/file
It will connect to the second board, read the /my/remote/data/file (change the file name) as it is being written, and spit the output on the terminal. You can use UNIX redirection to put the output in a local file, or to pipe it to a program for processing. Also on the remote end it doesn't have to be 'tail -f /my/remote/data/file' command. You can use any other UNIX command that will produce the output. For example you can run a program that reads sensors and writes the readings to the stdout (standard output).
I've never tried this, however I believe it can be done. Actually, I believe there is more than one way to do it. I mean, if I'm not mistaken this can be done with Ncat or by creating a virtual port with a package like ttypatch or with sockets network programming. I also believe that setting this up will be a little bit more difficult than with sftp. So I'd suggest you to try with the documents above and the methods mentioned in them.
Also, I will leave you a few links that I believe you might find helpful: