PIA and Mullvad should have equal speeds because they both have 10gbps servers and wireguard. Both PIA and Mullvad use ram-only servers exclusively. As for search engine captchas, I never get them with Mullvad. The main issue with PIA is that they were bought by a questionable company that previously developed adware. You can read about that here. Personally, I would never use a privacy tool that is owned by an ad company, even if they claim to have changed. I used them up until the acquisition, then switched and have been extremely happy with Mullvad.
The IP address that a request is coming from can absolutely cause captchas to be triggered. If the host is seeing a lot of bot activity from your IP, it’ll do that. That and blacklisting is why Mullvad rotates IPs.