I've used sharelatex and overleaf. I find them great. But what people in my field want are tracked changes features that you see in MS word. So deleted/added text highlighted by who changed it, comment boxes, etc.
I wrote SageMathCloud's collaborative online latex editor. Like ShareLatex, it's collaborative and 100% open source. There's a docker image for very easy personal hosting. SageMathCloud tracks all changes with a "TimeTravel" button for browsing history. You can click a "changes" button and get a range slider to see the exact changes (and who changed them) between any two points in time, with a display similar to github's diff view. It has split pane editing so you can edit two parts of the same latex document at once, along with forward and inverse search. There's also a full terminal (and Jupyter notebooks), in case you want to mix latex with computation/data, or want to use rsync, git, etc.
With latexdiff (included with your LaTeX distribution) it's really easy to produce "track changes" PDFs. (That's the entire purpose of this tool.) With git it's very easy to checkout the .tex file from an arbitrary commit.
There are even wrappers that integrate this with git, so just "git latexdiff HEAD~5 HEAD" will give you a "track changes" PDF between the current version and the one from five commits ago.
I've used this on complex papers where editors have requested it, and it works fine. Once I had to manually tweak the .tex file produced by latexdiff, but it was a very complex use case (packages added and removed between versions) and pretty easy to fix.
Use latex with git, say on github. You get all those features and more, just with a UI that separates them from the document.
I've collaborated on notes using latex before on github and PR discussions, inline comments, and git collaboration features like branching, descriptive commit messages and diffs, etc. are awesome for productivity.
That said, everyone will need to know how to use latex, git, and GitHub, so gdocs certainly has a simpler workflow.
