Technical advantages of either Configuration or Features over the other?
Watch Configuration for the future, because it more closely follows the model of Drupal 8. But I wouldn't suggest using it for now, because it is in alpha state, which means you need to be prepared to hack on it to keep it working, and you need to constantly update it, because it will not get formal Security Advisories if security issues are discovered.

Features is at 1.0, so it's a more stable choice for projects going to production soon, as you can trust that minor version updates will not break your existing features.