You run Browserify to bundle your modules offline, and then embed that bundle. With require1k you just embed the script and use one of the API methods to load your main module and everything is downloaded as needed. They are two different approaches.

require1k has a limited feature set (due to its size), creates a lot of http requests and is really suited for a small prototyping where you don't want to set up Browserify's build process. Browserify is what you should actually be using for production sites.