I never used Hyperbole back in the day so this is all fresh for me. I am also an avid org-mode user. The following feedback is based on about 48 hours of usage.
Hyperbole is a suite of tools. One of them is an outliner that overlaps quite a bit with org-mode. It has some interesting features like being able to link individual paragraphs as opposed to just headings/sub-headings but in most cases org-mode is further along.
But there are other tools in Hyperbole that might interest you including Acme-like string execution. For example if you do M-RET on the word README it automatically jumps to README without having to go through the rigamarole or creating a link in org-mode.
One of the nicest things about Hyperbole is that it's available everywhere. Org-mode is a mode and its features are only available in *.org files. For instance if you dropped into `eshell` or `ansi-term` and did `ls`, you can move point to any of the directory's contents, do M-RET (or Shift-Button2) and jump to that file. And that's just one example. Note that this means that all Hyperbole functionality is available in *.org files as well. To me, except for the Hyperbole outliner, that makes complementary not conflicting. It's Hyperbole *and* org-mode, not Hyperbole vs. org-mode.
Additionally, off the bat, I found it very well documented and for me that's a proxy for the quality of a package and the maintainer, Robert Weiner is quite responsive and really seems to want Hyperbole to take off. There's plenty more functionality that I haven't uncovered yet but due to ease of installation and quality of documentation digging into it is actually fun; much more discoverable than org-mode which has become this giant bag of random directives.
Hyperbole, even though it is old, feels like it is in its second infancy meaning it is open to change based on community feedback. As a practical note, once you install it doing C-h h d d will fire up a nice Demo which I is think is more fun than watching a screencast.