SMTP STS (Strict Transport Security) vs. SMTP with DANE.

The Internet Public Key Infrastructure (PKIX) is broken, but several solutions exist to fix some of the issues around transport encryption with TLS and x509 certificates.
In this webinar a deeper look is taken at two solutions: RFC 7672 “SMTP with DANE” and draft-ietf-uta-mta-sts “SMTP MTA Strict Transport Security (MTA-STS)”.
What problems are solved with these solutions? What is needed to implement MTA-STS and SMTP-DANE?
Is one solution preferable over the other, or should you deploy both?