Overleaf is a collaborative writing and publishing system designed to make the process of producing academic papers much quicker for both authors and publishers, from Writelatex Limited in London.
Overleaf is good to use in a lot of scenarios where something is to be written as a group. However, I believe that it is only good up to a certain amount of people working on the document at once. While I am unsure when it becomes too much, I got no doubt that there is a limit for when it is that good. Though normally, our group size of up to six people has been fine to work with in Overleaf.
I would recommend Vim in any scenario where text files have to be viewed, created, or edited on GNU/Linux computers. Regardless if you need to quickly change a few things in a configuration file, or you need to write up a full document, Vim is great. I wouldn't use Vim to view, edit, or create anything that requires "rich-text". In other words, if you need to format the text (bolding, font colours, word-art, etc), then Vim isn't the tool to use.
I don't consider the steep learning curve to be a hinderance on the overall usability. I would rate this a ten, but to be honest a lot of people do get hung up at the beginning and just abandon it. However, for people who have made the moderate effort to get over the hump, nothing can be more usable.
There is no commercial support for Vim. Thus, it will not get a mark beyond 5. However, community support is very good. You can easily find solutions for most of the problems in the community.
Overleaf promotes collaboration and has much better scientific formatting, which makes it great for research papers. It allows for much smoother and more professional looking documents, with easy to change and configure formatting. It is very difficult to insert mathematical formulas and long complex derivations in Microsoft Word, and formatting in Microsoft Word is also very finicky.
Vim's keybindings are a lot more complex than Notepad++. With that, comes a whole bunch of capability that Notepad++ just can't match. Emacs is comparable, in terms of capabilities--because Vim is built into so many unix systems, I chose to learn it instead of Emacs. Knowing both probably isn't a bad idea, but there's enough to learn in either camp to keep you busy
