The only difference is, that you're not "protected" by nat, so packets going back to you, can go back to you (but this is solved by a simple firewall installed by default on pretty much any ipv6 enabled CPE).

With ipv6 privacy extensions, your IP address changes every few minutes (withoin the same /64 network) so it's not a lot different (privacy wise) than today, wher that whole network would be hidden behind a single IPv4 address.