In IPv4 you do not notice it (it almost never triggers) because there is less tunnels and also because generally everyone does MSS clamping. In IPv6, you have the tunnel and not necessarily MSS clamping.
Two ways to tackle it:
- configure on the home router interface facing your LAN, IPv6 MTU less than you have on the tunnel (I have 1400 just because I like round numbers :-) Cleaner because works for (mostly) all protocols.
- configure the first hop router to do MSS clamping for TCP on IPv6 to 20 bytes less than what it currently does (if at all). This will work for only TCP, but that'll be the vast percentage of the traffic you are having problems with.