It sounds like are modifying the data in your database on only one of the two devices at a time. That simplifies your options. Using iOS7 on my iPhone4s, I routinely use drop box to wirelessly move files to and from my iPhone. I copy the file to a drop box folder, then use the drop box app to open the file using the "open in" option to open it in FileMaker Go. I get an option to either add a copy or replace the existing copy when I do so. I can select files from the "files on device" view in FileMaker and copy files back to drop box in order to get the latest copy back onto my computer.
It is my understanding that in iOS8 this has been made a bit less convenient. I believe the method still works but the "open in" option no longer actually opens the file, though it still copies the file into place.
You are correct PhilModJunk about ios8, it copies and opens Filemaker Go where you left it, so if you leave the last app open then you will be taking back to that app. Confused me the first time, though I had accidently copied over a database.