Next Gen Mail Handlers is a new breed that comes along with Email This Issue's Mail Account management.
Handlers of this type are composed of building blocks (actions). It takes algorithmic thinking to build up these handlers but they are ultimately simpler and more flexible.
Classic Mail Handlers are legacy handlers that have been available in Email This Issue for many years.
Handlers of this type follow the traditional ways of configuration: you have a bunch of fields and options in a single entity to configure the behavior of the handler.