What's the difference between the 2 different Rules pages in admin?
Entity Rule is not alternate to Rules


It simply acts as component which is, it allows you to set certain conditions and action on it and then this component can be picked by rule to run on certain event.
It gives another interface for rules action on "Entities" so you do not have to have rule administration permission if you belong to a role who has administration permission for certain entities.



  When do I use one over the other (to send emails when nodes are
  added/edited)?



If you want a user role with administration permission of content, and you do not want to confuse or simply give them permission to see all rules on site but you still want them to configure their entity specific rule, use entity_rule module.
You can also it for sanity of configurations, as it will bundle rules specific to entity on entity page, keeping default rules page more cleaner.