In general, the level of privacy/ anonymity should be pretty similar with IPv4 or IPv6 in the real world. You will be better off at some hacky, local IPv4-only ISP behind a huge "CG"NAT because they may not keep all the records or not for so long or whatever. You might be better off at a large mobile provider with IPv4 as a service over an IPv6 network, because the prefixes can change often and IPv4 is again basically a huge gateway hiding you to some degree. If you really need to be as anonymous as possible to most services online, use TOR or a series of VPNs/ SSH tunnels in different countries or whatever and a number of other anonymizing tools, browser plugins etc. Having IPv4 or IPv6 will not play a role as people usually leave huge amounts of traces all over the place.
For websites, for all these reasons, it is way more interesting to fingerprint you with multiple different aspects of your online presence. E.g. look here: https://amiunique.org/ or here: https://robinlinus.github.io/socialmedia-leak/
For most people and websites, IPv4 vs IPv6 for fingerprinting isn't very interesting because websites have better means and people usually don't really know/ care and most ISPs think they have a great business model handing out dynamic prefixes/ IPs and combining all that with CGNAT or NAT64/ DS-Lite or other gateways. Privacy extensions and local NATs of various kinds also don't help in having more visibility into that chaos. Actually, in my experience, most tracking currently is really, really dumb to such a degree, that I cannot be reliably tracked even if I want to (e.g. when using navigation like Waze) because for some reason, the app cannot get my position using GPS even after tens of minutes. The app still hasn't figured out, I live somewhere else now and hasn't offered me a new home address. It also doesn't recognize any pattern in my routine quite obviously. That would actually kind of be the point of the app, wouldn't it - it would make it more comfortable for me and it could serve me much better targeted adds, e.g. for good coffee in the morning? I also don't get very meaningful suggestions or adds for anything and I only use an add-block plugin. For those reasons, I don't think most websites are able to track me effectively and I don't worry about law enforcement much - I am not a journalist, nor a dissident, nor have I done anything in regards interesting to law enforcement or such.
I think, we all should worry a bit less and focus on fixing stuff all over the place so that tracking is more easily detectable and can be mostly disabled in such a way as to not hinder useful functionality. IPv4 and IPv6 as currently deployed are mostly "boring" in a good way. IPv6 tends to work just fine in places that want to make it work. So for most things, talking IPv4 vs IPv6 is like vim vs emacs or some other endless and rather pointless discussions. Not very informative or useful. We should be using what makes sense. IPv6 starts to make sense in most places, because it becomes easier to set up each day and IPv4 becomes more expensive to maintain. The real problems of IT are really elsewhere now and they are so plentiful.
You would laugh, but just doubling the amount of RAM in the computer today is an undertaking. You cannot get RAM with the same frequency and timing as is built into a computer just a few years old. Higher speed RAM doesn't "just work". No, you have to update the BIOS/ UEFI because they have support for newer RAM standards as it turns out and set the frequency by hand to enforce a downclock of the newer RAM - not really something a regular user would know how to do at all. All of this just adds up and the IT field is so complex nobody can reliably navigate it nor give any dependable estimates about anything. You have similar things way up the stack. Just try updating dependencies in a project (mentioned at length on the front page just a few days ago https://news.ycombinator.com/item?id=29106159). If engineers have to solve stuff, that should have taken 10 minutes for 2 hours instead, we have a major problem - we are just not getting stuff done, because we have been let down by otherwise solid assumptions.
For most people and websites, IPv4 vs IPv6 for fingerprinting isn't very interesting because websites have better means and people usually don't really know/ care and most ISPs think they have a great business model handing out dynamic prefixes/ IPs and combining all that with CGNAT or NAT64/ DS-Lite or other gateways. Privacy extensions and local NATs of various kinds also don't help in having more visibility into that chaos. Actually, in my experience, most tracking currently is really, really dumb to such a degree, that I cannot be reliably tracked even if I want to (e.g. when using navigation like Waze) because for some reason, the app cannot get my position using GPS even after tens of minutes. The app still hasn't figured out, I live somewhere else now and hasn't offered me a new home address. It also doesn't recognize any pattern in my routine quite obviously. That would actually kind of be the point of the app, wouldn't it - it would make it more comfortable for me and it could serve me much better targeted adds, e.g. for good coffee in the morning? I also don't get very meaningful suggestions or adds for anything and I only use an add-block plugin. For those reasons, I don't think most websites are able to track me effectively and I don't worry about law enforcement much - I am not a journalist, nor a dissident, nor have I done anything in regards interesting to law enforcement or such.
I think, we all should worry a bit less and focus on fixing stuff all over the place so that tracking is more easily detectable and can be mostly disabled in such a way as to not hinder useful functionality. IPv4 and IPv6 as currently deployed are mostly "boring" in a good way. IPv6 tends to work just fine in places that want to make it work. So for most things, talking IPv4 vs IPv6 is like vim vs emacs or some other endless and rather pointless discussions. Not very informative or useful. We should be using what makes sense. IPv6 starts to make sense in most places, because it becomes easier to set up each day and IPv4 becomes more expensive to maintain. The real problems of IT are really elsewhere now and they are so plentiful.
You would laugh, but just doubling the amount of RAM in the computer today is an undertaking. You cannot get RAM with the same frequency and timing as is built into a computer just a few years old. Higher speed RAM doesn't "just work". No, you have to update the BIOS/ UEFI because they have support for newer RAM standards as it turns out and set the frequency by hand to enforce a downclock of the newer RAM - not really something a regular user would know how to do at all. All of this just adds up and the IT field is so complex nobody can reliably navigate it nor give any dependable estimates about anything. You have similar things way up the stack. Just try updating dependencies in a project (mentioned at length on the front page just a few days ago https://news.ycombinator.com/item?id=29106159). If engineers have to solve stuff, that should have taken 10 minutes for 2 hours instead, we have a major problem - we are just not getting stuff done, because we have been let down by otherwise solid assumptions.