As long as your (production) config files are not checked in with the code, then little difference. The challenge then is: where do you store them?

Environment variables had the early upside of being first class in any virtually any deployment strategy - from Bash wrappers, supervisord to Docker and Kubernetes - so it's pretty much plug and play. For example, Docker has config files, but they're mounted to a specific place in your container, so that means your application is now married to that location.