Yes - you can use Mandrill for newsletters if you want to code your own subscription logic and store your own list of emails. MailChimp is quite a bit more expensive than Mandrill, but it does a lot more too. MailChimp stores more analytics than Mandrill does and stores it longer. It handles scheduling, batch testing, social integrations and content management in ways that Mandrill really doesn't. MailChimp also has analytics and profiles for list subscribers that Mandrill doesn't have.

If Mandrill does everything you need it to do and you can do the rest on your own, you should use Mandrill. It is, as you note, much cheaper.

I can't speak for MailChimp, but bulk e-mail requires a lot more managing - particularly for spam - than transactional.