Hi Didie,
Frankly, I haven’t used Mailerlite. As for the MailChimp, it’s overall a great solution and I had a very nice experience with it. However, last time I checked (2 years ago) there was not an out-of-the box way to let WP-site visitors to subscribe and get notifications of new posts via MailChimp. At that time I was contracted to code such a solution for a client. Things may have changed since then.
You also can use Jetpack for blog subscriptions. Just as in the demo.
Regards,
Paul