Actually, there is http://linuxbrew.sh/, which is a fork of Homebrew, if one insists on using brew :) An advantage of brew over apt et al. I imagine would be simplicity, e.g. you don't need to add PPAs, import keys etc. Though I should add that in my limited experience with linuxbrew, I still had to deal with custom flags/builds/whatever in case of compatibility/version problems.

With the benefit that you don't have to use an additional module/command (brew cask) to get functionality like "install Google Chrome".