The scrum template has been created specifically to follow the scrum process and terminology as closely as possible and was built as a collaborative effort between Microsoft and scrum.org.
The MSF for agile template was originally created as a generic process template for agile development.
If you will be doing Scrum, which at the moment is the most common agile process, then the scrum process template is the most logical choice.
If you want to follow another agile process, then MSF for agile might be a better fit, since it should be usable in most agile processes. The naming might not completely match, but the process can probably be mapped to it.
Differences are explained here: https://msdn.microsoft.com/Library/vs/alm/work/guidance/choose-process