Since Josh mentioned this tonight, I'd like to share my experiences with it since March. I admit I don't remember when I enabled it, but I think it happened thusly: Blizzard introduced IPv6 access in January 2012, I discovered it some months later when I tried Cataclysm for a few weeks, but they did not enable it for 6to4/tunneled address ranges (like mine), so I never had the opportunity to test it. As such, I must have enabled it during that time, forgot about it, and then discovered it a couple weeks after re-upping my account.
If you're using native IPv6 (depends on region and ISP), your experiences won't match my own because it should perform similarly to IPv4. If you're using a tunneling provider like Tunnelbroker (or similar), your game play experience will vary. Here's an example of my usual post-peak latency over IPv6:
This latency is, on average, about double what I normally see over IPv4. Unfortunately, during peak hours, it'll usually spike to ~300-500ms (about half a second). Tunneling providers essentially provide access to the IPv6 internet by encapsulating IPv6 packets inside IPv4, thus increasing overhead, and unless you can find an endpoint nearby, you'll have a base latency level added to your existing IPv4 connection consisting of the latency between you and the IPv6 endpoint. For me, this is usually negligible (~10-20ms due to peering agreements with my ISP and HE.net), but HE.net's endpoint I'm using has had a recent history of instability for reasons I'm unaware: Load, my local configuration, local network traffic on my network also using IPv6, other traffic external to my network, or the fact that it's located in Los Angeles and probably everyone in this part of the country picked it as their endpoint.
All told, it hasn't affected my gameplay all that much. On the rare occasions we've done dungeons in the evening, I've noticed periodic spikes that affect spells, but it hasn't yet cause too much grief. I wouldn't recommend it if you were doing something important yet, but the tunnel providers, Blizzard, and others have worked together in the years since it was enabled on the game servers (2012ish) such that even tunneled IPv6 addresses (beginning with a 2001 prefix) work fine.
Again, your experiences may vary. If you're thinking of trying it over a tunnel, just be aware you might be disappointed and it may be necessary to revert to IPv4.
Note that even some native IPv6 routes may use different peers which could improve or worsen your latency. Usually this isn't the case, but for larger providers I've read reports of native IPv6 appearing worse than tunneled connections. We're sadly not at a point in time where complete IPv4 cutoff can occur, but we're getting there slowly.
To be honest, I think the only way we could guarantee a next day switch to IPv6 is if all porn sites cut off their IPv4 access completely.