Looking for a good repository for academic drafts
If you are familiar with LaTex, use it with git.

Edit and mess around with paper on master branch, and push some good, meaningful and confirmed improvements on your work into release branch. 

If you need a repository private until you decide to make it public, use Bitbucket or GitLab, instead of github. They provide free private repository. When you finished your paper, you can change repository settings to public.

I am not sure whether Diff-ing PDFs---your previous and current paper---is easy problem or not. But you can choose a solution among several: pdfdiff, DiffPDF, pdf-diff, diff-pdf and etc.