Why choose nodenv?
Because nodenv was forked from rbenv, many of the reasons to choose nodenv over others are similar to why one would choose rbenv over rvm. (Nodenv also inherits a much longer battle-tested history than others.)
One of the biggest reasons to choose nodenv over the others is that nodenv can automatically select the appropriate node version for a given project. Neither nvm nor n have auto-switching capabilities out of the box. They both require some form of 'use' command to activate a given version; which lasts for the lifetime of the shell (or until another version is activated).