I've been Googling this for about 20 minutes and haven't found anything relevant. On Linux, the configuration file gai.conf allows me to set getaddrinfo() to prefer AAAA records over A records when doing a DNS lookup. I can't find an equivalent on FreeBSD.
All I found was this page, which says "FreeBSD prefers IPv6 if a DNS query results in IPv4 and IPv6 addresses being sent back (A and AAAA RRs)". This doesn't seem to be the case.
I know for certain that v4v6.ipv6-test.com does have both AAAA and A records, but FreeBSD is preferring to connect via IPv4. When I put an IPv6-only address into my browser (v6.ipv6-test.com), FreeBSD does connect over IPv6 as it should (so I know for certain that both IPv6 and IPv4 are working fine, it's just a matter of preferring one over the other in a DNS lookup).