As Ian said, component's opinions encourage more modular, better code, and allow you to do what Web Components only now are promising within the DOM itself: bundle together templates, css, code, data, etc. And it does this without imposing a framework. For instance, if you have a pure javascript library, it is extremely easy to package for both component and NPM. Most of the UI components are framework-independent and that is encouraged. The component ecosystem and community is fantastic. And it's not sponsored by a corporation on the NYSE :) These were the main reasons I was attracted to component. The learning curve is a bit steep, but getting better all the time.
2. component doesn't just manage 3rd party packages - it helps manage your internal code/styles/templates as well. see https://github.com/jonathanong/bigpipe-example/tree/master/c.... keeping CSS/JS/HTML for a component of your site in completely separate folders is a thing of the past.
3. it's less adopted because it doesn't have Twitter's marketing and man power. TJ also hasn't had the time to document or market it well. it's also much more difficult to teach (well).
4. i hate requirejs due to its unnecessary callback and defining modules through function arguments. if i weren't using component, i'd use browserify. i have not seen any non-requirejs implementations of a build step, and i'd rather have a single step than two.
5. it's easier to share code between node and the browser. with requirejs, it's a little harder, but it's easiest with browserify.
6. most bower packages are bloated and require other large dependencies like jQuery, and I can't filter through that. component modules, on the other hand, tend to be very small, lightweight, focused, and overall better quality. for example, https://github.com/yields/select is becoming pretty excellent, much better and less bloated than select2.
7. bower packages tend to come with excessive amounts of options (because people request them, ex. select2) and excessive boilerplate code (because people want it to look good right way, ex Font Awesome). component packages tend to be the opposite - minimal, structural styling and very few options.