Fresh mu/mu4e user here. The advantages over mutt/neomutt are that your e-mail now becomes the part of the same consistent UX of Emacs, and then every improvement to any of your workflows in Emacs is automatically inherited by your e-mail workflow. This depends on how much you like customizing Emacs and/or writing Emacs Lisp to solve your problems. Some practical examples include:

- org-mu4e & org-notmuch will let you link directly to your e-mail messages from your org-mode files; potentially useful if you're using org-capture to quickly add TODOs and notes.

- it's trivial to add any kind of template responses, template subresponses, etc.

- you can make Emacs automatically do things in response to particular e-mails, or you can compose/send e-mails directly from any elisp code

Emacs is a fully programmable environment with lots of existing software packages and the best interoperability story I've ever seen.