Both have the largest communities for gaming, it really comes down to how much control of your system you want.
Bazzite is immutable, so all core system files are read-only, so you have limited access to them, but you can't break anything. You'll largely be using flatpak apps, appimages, and then anything else you're either going to layer the RPM (fedora-based) application into your system, or using Distrobox to handle deb or Arch-based packages (kinda like emulation). Some packages that have core system access might not work via any of those methods, and for some of the popular ones they created some
ujust commands that run scripts to automate those installs like DaVinci Resolve (video editing app). Bazzite automates quite a bit since it just downloads new images of your OS, and then even at boot you can select the previous images if the new image breaks something.
CachyOS is the opposite, it gives you pretty much full control over your system, it's pretty bleeding edge cause it's Arch. Sometimes that can create instability, but for gaming CachyOS is much more stable than vanilla Arch, and they give you a GUI-based way to install Nvidia drivers. Only difference isPikaOS and Bazzite have ISOs that come with nvidia drivers pre-installed, while you have to manually select that stuff during the welcome setup I think with CachyOS, but should be pretty easy. Most of these gaming distros have maintainers that know each other, and cross-pollinate features. CachyOS kernal optimizations have been copied, PikaOS's GUI device manager was copied across these, and they all give you a handy list of useful gaming apps to install out of the gate.
I liked Bazzite, would recommend for a portable or living room setup since it's so automatic, but I like having more control of my system so I jumped to PikaOS. What I've seen and heard is CachyOS is pretty similar, so if Pika didn't exist I'd be on that with fellow Linux Bro
BeardSpike
. You could always use Bazzite as a learning experience, since it's easiest to use, and see if the limitations actually limit you though. Go with KDE or GNOME though, other choices are either more complex (Hyprland), a bit too early (Cosmic), or old (XFCE).