When comparing Mu4e vs Atmail, the Slant community recommends Atmail for most people. In the question“What are the best self-hosted webmail clients?” Atmail is ranked 5th while Mu4e is ranked 6th.
Ranked in these QuestionsQuestion Ranking
Pro Can write rich text emails
Using the (beta) org mode, Mu4e can compose fully rich text emails.
Pro Built-in Autocomplete
Doesn't require you to import address books for autocomplete, learns from your emails just like Gmail.
Heavy actions never block emacs, unlike most other emacs email clients.
Pro Fully Search Based
Mu4e has no folders or other organizational tools, rather it relies on very fast search queries to help you find your mail.
Pro Intuitive interface
Pro Powerful yet easy to use admin tools
Pro Browser, desktop and mobile versions
Pro Plugin support
Con Bad UX
It's slow and unintuitive.
Con Closed source
Appears to be a proprietary product.
Con Not free
As in beer or software.