Anyone on PC wanting to do this I would advise skipping the backup tool and simply setting up a dropbox account that syncs your character data folder. I do this and all my settings and hotbars are automatically synced between the various PCs I play on. This wouldn't work for consoles though.

SE did offer a tool of this nature for the initial PS3 to PS4 transition. In theory that could be re-implemented to be used as a backup/sync service as the OP wants but it would require quite a bit of space. My character data is 21MB in total now and it continues to grow as I create new armoury sets or new customisable features are implemented. That would be pretty hefty if every player stored a backup of that folder for each character they had.