Goodreader isn't dead. Do your
research and get in contact with the dev.
I recently got in contact with them and they are just about done finishing their beta period. Once done (and no issues found) they will release the app to the public. This update will be free from what they told me. Here's their reply to my email:
The GoodReader 4.0 update will be free for existing users. The update is in a beta testing period now. Currently we have all the beta testers we need for this. We anticipate a 2 week beta test period and then the final release date for the update depends on how many issues may be discovered, and of course fixing those issues if necessary.
Thanks for your patience while we work to complete the next GoodReader update!
On another note, it isn't easy to just update/re-write an entire application. It takes a lot of work and dedication (which is why it is understandable why many choose to charge for the new version). Simply stating that an app has become crapware because it hasn't been updated it is unwarranted, especially if you haven't bothered figuring out why the app hasn't been updated.
In regards to the difference between Documents and Goodreader, the main one is annotations. Documents has limited annotation capability (such as highlight) where as Goodreader will allow free handwriting, stamps, signatures, etc. Goodreader is more like Readdle's old PDF Expert.
Regarding Sync in Documents, it works the same way as in Goodreader and PDF Expert. You connect your cloud account to the app, find a folder, and set up 2-way sync. Now every time you make changes to that cloud folder and press sync in the app, all changes will download to the tablet. Do note that the sync is 2 way and not 1 way; hence, if you delete a file in your sync folder on the tablet, it will delete from your cloud account, and (if you're like me and have your cloud accounts linked to your Finder and not the Dropbox folder), it will delete from your computer.