FTL: Advanced Edition is now available on PC and iPad, giving the galactic roguelike new life. Unfortunately, save files can't be accessed both platforms, but according to a bold user, it does appear that there's a way to transfer save files from one platform to the other.
The walkthrough comes from Stack Exchange (via Touch Arcade), which first instructs users to locate their save files and then locate a tool to upload files to the inside of an application sandbox on an iPad.
"Open the FTL app in your iOS file explorer," reads the walkthrough. "Browse to the FTL app and you will see a file structure that includes a Library/Application Support directory with a prof.sav file. This is the default save file, but if you have enabled Game Center, there will be a separate prof.sav file under each player ID inside the players folder here. Make a backup copy of the files here, if you wish to be on the safe side. It would also be a good idea to kill the FTL app on your iPad if it is currently open, to prevent the game from overwriting your changes when you save and quit. (double-press your home key and swipe it away on iOS 7, or press the X on iOS 6)"
Upon finding the prof.sav file on your PC, there will be a separate ae_prof.sav file alongside it. The last step is to copy that ae_prof.sav file to the iPad, under the same folder where the prof.sav was located. Delete the prof.sav on the iPad and rename ae_prof.sav to prof.sav.
Unfortunately, there is currently no way to merge save files between the PC and iOS versions of FTL at this time.