Looking only at the technical differences, hCaptcha lets enterprise users like Proton locally scrub any info like IPs prior to sending to hCaptcha. It can be set up so that the user makes no direct connection at all to the service, and the code runs inside of a sandboxed IFRAME.
As for false positive vs false negative rates, not sure what you consider too high. We've been able to demonstrate FP rates under 0.005% when measured against known-good/bad signals from customers, which is as good as it gets.
(disclosure: work there)
but more importantly, in the long term, it needs policy and legal progress. it needs to be costly and international (via treaties/sanctions).
Until they get broken by botnets and we are back to where we started by using Google ReCaptcha.
also, captcha in general shifts burden onto and penalizes legitimate users, especially privacy-conscious ones, in addition to malicious ones. that is, false positive rates are too high to achieve acceptable false negative rates.
it would be better not to use a centralized captcha service, if one must be used at all.