Going with JSSE does have the downside that it's less widely used. Browser makers don't patch it with the latest gizmos like they do with OpenSSL. However, it's at least got a full time development team (unlike OpenSSL until very recently), and ultimately if there are odd conformance bugs lurking the only way they'll be shaken out is by people using it for real. Passing the Qualys test is a good start, but for now my little website is ideal because it is unlikely to ever be popular enough to have serious scaling issues and I can tolerate some incompatibility with odd clients.