What happens if you edit a file? Does it get copied to all the other devices or does it get overwritten by the backups of that file?
Then on the other hand...
What if you edit a file and it becomes corrupted? Does it then overwrite all your backups of that file? In which case they're not really backups are they?
Then also...
What if you want to delete a file? Does it delete all backups of that file too? or does it keep replacing the deleted file until you delete all the backups as well?
What if deletion is accidental?
You can see in each case how a syncing system between devices could potentially lead to a great deal of hassle.
This ^^ is why I prefer proper backups, rather than syncing between devices.....
Proper Backups - rely on you remembering, rely on single devices, does it do versioning without you having to do it manually?
Dropbox - All computers have copies of the files, all mobile devices can browse the files. Dropbox does versioning automatically (you just need to turn it on)...
https://www.dropbox.com/help/11/en . I sync between 2 desktops, 2 laptops, I have shares with a team of developers and shares with other people. I have about 20Gb in dropbox and I haven't had a single corruption. How to recover deleted files....
https://www.dropbox.com/help/296/en. Again you may have to turn it on.
If you delete a file, it gets deleted everywhere, but you can recover it.
Automatic is always better than manual (unless you do it a really stupid way)
Dropbox isn't the best solution for backup, it is the best solution for transferring files and syncing files.
If you want backup, look at crashplan, Amazon Glacier etc.
For you, I would transfer using dropbox, but backup using your 1TB drive as you like your manual way for peace of mind.