Organizing one's work is a bit different for each person, and since you have done a lot of work in C, certainly vi and clang files are more your /modus operandi/. However for those of us with LISP backgrounds, Emacs is definitely more suitable.
What you gain with org-mode is quite a bit:
Org-bable which allows you to write outlines with blocks of text that can call external scripts. This is a bit like a Mathematica workbook, with text notes and evaluations, but you can call to Python, Ruby, or whatever language you want.
You can export an .org file into many different formats. LaTeX, HTML and OpenOffice format are what I use most often. Note that you can modify the template to export to any custom format you want. What is very useful are the Beamer templates, where you can turn an .org document into a slideshow very easily. This is a killer feature for anyone who has to lecture often and needs a quick way to get his notes on some slides that look quite professional.
Org-mode also has an agenda, calendar and even contacts if you want to store them there. You can provide links in your agenda to a specific part of your file, so you can click on the TODO link and go immediately to what needs to be done. This is extremely valuable for a large project and saves a lot of time.
There is also org-capture for those moments when you are fixing one file and you need to remind yourself to refactor a function in another file. This helps avoid many bugs especially in a large project where the function definition can be somewhere else. You can also capture any sort of text. When looking up documentation I often capture the web page and put it in a NOTES.org file in a project, especially when it is something obscure that I don't use that often. These notes can also have links/todos, etc. making it very practical.
Also since I do email in Emacs [mu4e], I can simply make a TODO from an email with org-capture, and it goes into the agenda. In the agenda I have a link to the original email and to any other file or notes that I add to this task. This is very handy with bug-reports and things of this sort. Also, I can search my agenda files to see if anything like this has happened before, etc. It really helps to be able to do this without having to be online like with many bug-tracking software - which is very helpful when on a commute in the train.
These are just a few things that you would gain with org-mode, but really there is no end to the customization you can do. It is all written in plain-text and controlled with elisp. I like the fact that with this one tool [Emacs] I can do so many things, so it is worth the time to know the tool well. It also can expand to do whatever task I need to do. The plain-text format makes it possible to even employ outside tools, such as sed and awk, if I am not inspired in elisp at the moment. To do all the things that I do in Emacs would require learning several different tools each with their own document format and key-bindings and wouldn't even necessarily be adaptable to the task at hand.
On the other hand, you do have the obligatory xkcd:
https://xkcd.com/1205/