BTW, as kind of a follow-up to this, I think the most important finding to report--for those who only use one model, as many people seem to--is just how much more often Claude seems to be extremely confidently (and even insufferably) wrong than any of the other three big models (all of which I use quite often... yet I only pull out Claude when I've given up hope in a problem and are looking for out-of-the-box brainstorming).
And like, it does this despite it speaking in extremely dense math, which both makes it sound correct and requires a lot more effort to prove when it is wrong... yet, it isn't actually correct more often, and so that time sink just isn't worth the benefit. I then think many people--including people who can speak math (as can I)--just stop bothering to check everything, as if you come across a human who speaks like this it probably does correlate with slow and careful thought that helps prevent errors.
Instead, Claude has the mistake rate of a somewhat accelerated beginner impossibly combined with the language of an expert professor; and we as humans just aren't good at that combination: it becomes very dangerous and makes it take longer to spot its egregious mistakes and trained-in biases. If you have to use Claude, I thereby claim you really need to have a team of not-Claudes to help insulate you from this, and Gemini (while being a bit senile) is a lot more collaborative and approaches problems in ways that makes it harder to get tricked.
(To translate this into more of an engineering analogy: Claude always feels to me like the engineer who put more effort into learning how to program in functional languages than into how to actually develop working code, and then confidently presents you answers in Haskell or Lisp that never quite work. To find their errors is then very costly. In contrast, Gemini feels more like a Java or Go developer who knows they are a cog... that's helpful! <- Which maybe just goes to show that AI has finally turned me into a manager, omg.)