I should point out that I am not involved in the development of AppImage, I am just an application developer that uses the AppImage format to release their application for Linux desktops.
AppImages are not comparable to .deb files at all. Firstly the .deb format is specific to Debian Linux and its derivatives. They do not work with Red Hat based distros or Arch based distros. Plus depending on the libraries that the application requires, a different .deb file will be required for different versions of the distro. For example the application developer may need to make a .deb for Ubuntu 14.04, another one for Ubuntu 16.04 and another for Ubuntu 17.10. From a developer’s point of view producing .deb files to share an application is a nightmare, I know as this was the first approach that I tried to take with my application.
If you want to compare AppImages to something it would be better to compare Snap or Flatpack packages which use a similar concept of bundling their dependencies and work on most Linux distributions.
~/bin is just a folder called ‘bin’ in your home directory. Linux traditionally keeps its application binaries in a directory called ‘bin’, usually /usr/bin or /usr/local/bin, so this does make some kind of sense.
appimaged not only makes the AppImage executable but it installs/removes the AppImage desktop files for you. appimaged is a work in progress as I understand it.
To install appimaged you would do something like:
wget "https://github.com/AppImage/AppImageKit/releases/download/continuous/appimaged-x86_64.AppImage"
chmod a+x appimaged-x86_64.AppImage
./appimaged-x86_64.AppImage --install
When I tried it it worked well for me.