Moving between Spring Config Server and Azure App Configuration is rather easy. The key item to key in mind is that Spring Profiles map to Azure App Configuration labels. Then Azure App Configuration allows for import/export of properties/yaml files either via the cli or the Azure portal, just make sure to set the label as the profile.
Azure App Configuration has spring-cloud-azure-appconfiguration-config, a provider library that supports loading and refreshing of configurations. This is also a Spring Web library that supports auto refresh.
There shouldn't be any feature that Spring Config Server has that Azure App Configuration doesn't. And Azure App Configuration supports config store replica for added redundancy if needed.
I'm the main developer on the Azure App Configuration Spring library. If you find any feature missing that you need create an issue on the azure-sdk-for-java github repo and we can look at adding it.