Be more specific. The Intents are a kind of API.

If you mean REST APIs, one advantage that comes to mind is that Intents should require less integration on the server. Just write a callback that handles the expected data, and don't worry about integrating plugins.

The key difference is that intents are generic and resolved by the client based on the user's choice. So, instead of a "Share on Facebook" button, you would just put a "Share" button on your site. When clicked, the browser can fulfill the action using any site it knows about that implements sharing. It somehow asks the user which site to use.