Mess with multiples Emacs distros (Homebrew)?

I have recently got a new copy of Emacs on a brand new macOS setup as follows, using the Homebrew package manager:

brew cask install emacs

I also wanted to try Emacs Mac Port, so I fired up my terminal and typed

brew tap railwaycat/emacsmacport
brew install emacs-mac

but lot of symlinking error appeared.

I thought it was a bad idea to let Homebrew manage so similar packages, and removed emacs and emacs-mac with brew cask uninstall emacs and brew uninstall emacs-mac.

Have I done a mess? Should I have done something else other than brew cleanup and brew doctor, before installing again the standard Emacs distro with brew cask install emacs?

If you don't want to use Homebrew, you don't have to. This is really a matter of taste. You can use Homebrew or not. You can build the application from source or you can download from GNU here or Emacs For Mac OS X here - both yield the latest versions.

If you want to use Homebrew, I recommend that you use:

brew install emacs

then link the binary if you want to run from terminal, this can be performed via:

ln -s /usr/local/Cellar/emacs/26.2/Emacs.app /Applications

If you don't want to use Homebrew, use one of the binaries listed above. Keep in mind you can always link them later if you want to run the latest version from the command line.