Free tools such as KDiff will perform a differential analysis on files and even show exactly which lines have changed. However, KDiff doesn't provide any ability to separate the changed files from the ones that don't need to be translated again. Fortunately, there is another application called Araxis Merge (Windows and MacOS supported) that does allow for this ability. At the time of writing, it's $129 for one standard licence.
Like Kdiff, you can run a recursive directory diff to find all the changes in all the files. However, once you have done your folder comparison, you can also select all the altered files (using Select Rows > Selected Changed) and copy them to a new "specified folder." Using this method, I was able to grab all of the XHTML files that have changed since we last did a complete document translation.
Note that this method DOES NOT copy new files. You will need to go through manually and copy the files that have been added. These files appear green in the Araxis folder comparison view.
I did run into some hiccups in Araxis, For example, a bug that often causes the right-click context menu to not appear and consequently hang the application. However, I was able to work around it and get my work done.