Not really as far as I can see.
- Where sites/services support IPv6 and IPv4 ("dual stack"), client devices will connect with whichever is fastest.
- Where a site only supports IPv6 you can use the site - not many sites though, just test and proof of concept sites.
- If a site only supports IPv4 you will continue to connect.
Bascially things just work the same as before.
Now, as an experiment, I did disable IPv4 on one of my devices so it was IPv6 only. It was amazing how many sites don't support IPv6, so this experiment only lasted about ten minutes before I gave up and turned IPv6 back on...