Whether one has more benefits than the other really depends on your organisation. Some organisations prefer the digital certificate because it is more familiar to a traditional certificate. On the other hand, some like the digital badge because it is a more modern approach. And so, some like to use both to get the best of both worlds.
Regardless of how you choose to display your credentials, the key benefits are that the digital credentials (a badge, a certificate, or both) cannot be forged, they are easily shared and always display current information.