require-stylify

This package is DEPRECATED. Find packages for styles under active development here. require styles in your browserify builds, same as you require your js files:

require('./less/main.less');
require('./sass/sassFile.scss');

This will get transformed into:

appendStyle('/less/main.css');  //and it will compile the required less file into this css obviously
appendStyle('/sass/sassFile.css'); //and it will compile the required sass file into this css obviously

appendStyle global is defined in https://github.com/capaj/require-stylify/blob/master/append-stylesheet.js

Should work with css, less and sass(only scss files are supported though).

why use this rather than node-lessify

Because this creates a css file on your filesystem and it appends style element with href rather than just appending styles directly into your html. This is better, because your generated less/sass sourcemaps still work. Also I believe having separate CSS and JS is good thing even though you end up with one extra file(your main.less/main.sass). I personally don't change css styles as often as JS files, so when you have live web app with caching, with most new builds, users download only JS bundle and their old cached CSS doesn't need to be reloaded from the server.