I am reading the documentation for both push using TLS certificates and push using authentication tokens
But besides explaining how to configure each, the articles don't really explain the differences or pros/cons of both approaches. Can somebody explain them to me?
Token-based authentication is newer and essentially simplifies APNS authentication. It is based on a public and private key pair that you can generate on your Apple developer account.
Here are the main reasons why it is simpler:
A good source of intel is the 2016 WWDC video regarding APNS: https://developer.apple.com/videos/play/wwdc2016/724/