Performance wise, I doubt there’s notable difference.
I’ve tried both, and honestly Bazzite OS is on a league of it’s own.
Nobara has updates with breaking changes that require manual steps to avoid bricking your installation.
Bazzite on the other hand immutability makes it a freaking indestructible distro, and for a gaming machine, that is a good thing.
Bazzite’s CI/CD automated builds helps them release upstream improvements way faster, for example… they are already on Fedora 40.
It also comes ready to go out of the box. The experience is amazing. The only drawback is having to reboot to apply changes to the system. But the many benefits outweight this inconvenience.