Curious what you need this for
Just to spot check and one off manually transfer files?
Typically I just run good old rsync and let it do the magic, all commandline.
So if you need the spot check manual thing, SCP is what to use... Encrypted, data not flying out in the open.
To make it mega Windows-like, get FUSE enabled on your VPSes. The install sshfs and map the shares between the two remote hosts.
Some text panel file manager like Midnight Commander (yes there are others) can be ran on either VPS and navigate the local directory on that server and the SSHFS mapping of the remote server.
From there it is pretty self explanatory to copy, delete, etc.
Hope that helps.