Advantage is that most of the time, you have a fairly new browser engine available for your app, that is not tied to the OS version (especially important on Android). Also doesn't require embedding an 50MB engine (Crosswalk) in your app.

Disadvantage is that as an app developer you're not guaranteed to have any specific version available. Some devices never upgrade the pre-installed version automatically. The user is also able to switch between the Chrome webview and an OS webview on some devices (in developer settings, so it's not common). You can add checks in your app and direct the user to the update links, but requires quite a bit of work to do well.