Generally speaking, MAMP requires you to install all of the server components to your local machine natively (mysql, apache, etc) which makes it extremely hard to mirror a production environment.
Like Local, Vagrant is a virtualized solution – meaning you can more closely (or exactly) match production. The challenge is just with configuration and complexity. Want SSL to work? You need to configure it. Etc, etc.
With Local, we’re aiming to be both powerful and simple to use for the case of building WordPress websites locally (you should never say “painfully steep learning curve” haha). We support features like Demo URLs (tunneling) and local SSL out of the box, without having to configure anything. And of course because it’s powered by Docker we can exactly match a production environment.
We believe Local to be a modern solution with a rich feature set, and are committed to building the single best Local WordPress development environment around.