Perhaps the most striking difference between a contemporary IPv4 network and an IPv6 network is that on the former, many hosts are likely to be “hidden” behind a NAT router (7.7 Network Address Translation). On an IPv6 network, on the other hand, every host may be globally visible to the IPv6 world (though NAT may still be used to allow connectivity to legacy IPv4 servers).
Legacy IPv4 NAT routers provide a measure of each of privacy, security and nuisance. Privacy in IPv6 can be handled, as above, through private or temporary addresses.
The degree of security provided via NAT is entirely due to the fact that all connections must be initiated from the inside; no packet from the outside is allowed through the NAT firewall unless it is a response to a packet sent from the inside. This feature, however, can also be implemented via a conventional firewall (IPv4 or IPv6), without address translation. Furthermore, given such a conventional firewall, it is then straightforward to modify it so as to support limited and regulated connections from the outside world as desired; an analogous modification of a NAT router is more difficult. (That said, a blanket ban on IPv6 connections from the outside can prove as frustrating as IPv4 NAT.)
Finally, one of the major reasons for hiding IPv4 addresses is that with IPv4 it is easy to map a /24 subnet by pinging or otherwise probing each of the 254 possible hosts; such mapping may reveal internal structure. In IPv6 such mapping is meant to be impractical as a /64 subnet has 264 ≃ 18 quintillion hosts (though see the randomness note in 8.2.1 Interface identifiers). If the low-order 64 bits of a host’s IPv6 address are chosen with sufficient randomness, finding the host by probing is virtually impossible; see exercise 6.0.
As for nuisance, NAT has always broken protocols that involve negotiation of new connections (eg TFTP, FTP, or SIP, used by VoIP); IPv6 should make these much easier to manage.