I'm currently using Mailchimp to send out newsletters. I send out two types of Newsletters....
1 - a summary of each class the day after a class takes place sent only to current students
2 -a weekly newsletter sent to all newsletter subscribers
I also use the Mailchimp form on my website for guests to sign up... also on FB Page for sign ups.
Mailchimp also takes care of removing people who want to be removed and confirming they want to be added to newsletter list.
I believe eNewsletter will do all that Mailchimp does. I did some searching through the forums and saw some folks are using both - so I wasn't sure how they worked together - if at all.