I think you’d be fine with either, but in the end it comes down to how “hands-off” you want to be, or how much customisability, flexibility and performance you’re after. Unlike Manjaro, Cachy is closer to Arch, which means things may on rare occasions break or may require manual intervention (you’ll need to keep up with the Arch news). Bazzite on the other hand is the polar opposite, being an immutable distro - updates are atomic (they either work or don’t, and in case an update is no good, you can easily rollback to a previous version from GRUB); but this also means you lose some customisability and flexibility - like you can’t run a custom kernel or mess with the display manager (logon screen) etc, and you’ll need to mostly stick to installing apps via Flatpak or Distrobox.

Overall, if you’re after a console-like experience that just works™, then choose Bazzite. On the other hand, if you’re a hands-on type of person who likes to fine-tune things and is after the best possible performance, choose CachyOS.