Updates:
Now ShareLaTeX and Overleaf are teamed up, so we do not need to worry about choosing which. We just need to use the merged online LaTeX Editor here: Online LaTeX Editor Overleaf.
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ShareLaTeX is an online LaTeX editor that allows real-time collaboration and online compiling of projects to PDF format. Overleaf (formerly called WriteLaTeX) is another popular online LaTeX editor that allows collaborative LaTex editing. See the post Comparison: ShareLaTeX vs Overleaf (formerly WriteLaTeX) for more details about the comparison.
Some main points from the comparison:
ShareLaTex:
- word count
- compiles faster
- autocomplete is more robust: it works with package and custom commands
- It doesn’t spawn multiple browser windows/tabs like Overleaf
Overleaf:
- many templates for all kinds of documents and scientific journals
- support for collaborative editing
- word count is supported now
- the free version supports Git. It is possible to clone your project to your computer, work on it offline, commit your changes, pull new changes, etc.
- you can download your bibliography directly from Zotero (so you can just click refresh, rather than export a bib file from your computer then upload it).
- autocompile and better editor/preview position sync.
Main differences:
- about the use of BibTeX:
Overleaf gives you popup access to a search windows when typing \citep{}
, making easy to find the key you want to use; while ShareLaTeX does nothing.
- for privacy some users probably preferred ShareLaTeX because the documents are private. In free Overleaf, whoever has the document url can edit, even though now
- free versions comparison: Overleaf Plans and Pricing vs ShareLaTex Plans & Pricing
- free version of ShareLaTeX:

My conclusions:
I have tried both, and I personally prefer ShareLaTeX. ShareLaTeX is better than Overleaf because of the slightly better feature set.
In ShareLaTeX, even in free version, your projects are private. But in Overleaf you need to use Pro version to get this benefit.
ShareLaTeX is better for users with LaTeX experience. Whereas Overleaf is good for users who have few LaTeX experience, because it supports both Rich text and LaTeX.
I have the similar conclusion as what this post describes: ShareLaTeX and latexdiff are two LaTeX gems. See my post for the usage of latexdiff.
(Thanks Guido for recommending ShareLaTeX and Overleaf to me.)