It seems hard to find an FTP client that does server-to-server transfer. Finally found this gem, whose name I forgot. Its been a while since I last used it, years ago. FlashFXP is one of those tools so I'm about to start using it again. The idea is to utilize FTP servers for web application deployment and a tool like this seems to be a very important piece of the puzzle.
Since there is no free version, I decided to look further. As per Wikipedia page (link), I decided to try CoreFTP, which is both free and supports FXP. Testing it gave me a warm, fuzzy feeling of a smooth deployment from Continuous Integration server to Test or Production environment.
Well, it turns out the things can get even better - FireFTP is a Firefox addon that supports FXP! (link)
The problem, however, is that it does not work with my 4.0 build of Firefox. Continuing search...
BitKinetix (link) looks promising. Need to test later.
Another thing I need to confirm is whether FileZilla server supports FXP at all. If not, I might utilize BitKinetix and WebDAV->FTP transfer.