Review: Subversion
How it will save time: SVN checkout is the fastest way of maintaining files on a webserver. It is also secure.
Comments: Sure FTP apps have "sync" buttons but do you trust them? How many times have you dragged and dropped a file into the wrong folder using FTP? Once you overwrite a file you can never get it back. Never mind the security gap everytime your files get transferred.
The checkout feature in Subversion (SVN) allows you (via ssh) to synchronize your local repository with the one on your webserver. You work locally. You commit. Then you fire off a command to update all your edited files. That means all the edits are versioned properly so you simply rollback with no worries if something goes wrong. And if you have mutiple people working on a site they can all upload concurrently without fear of overwriting something important.
It takes some know-how to install and some command-line prowess to use but SVN will improve your workflow dramatically.