Running from a Live image is not going to be performant for a number of reasons I won't get into, but mainly that you'll have a loop with some crucial systems back through that USB still. Not absolutely everything is always loaded directly into memory unless you ensure that it is.
The USB medium you're using is probably slow, so any I/O access to that drive is going to cause performance hits briefly.
That being said: there isn't going to be any appreciable difference between your two distros in a way that will blow your mind. The "gaming distro" is kind of a farce/myth, with package selection and user interaction being the biggest differences between them.
If the distros are on the same general kernel line, you'll get very similar performance between them (check Phoronix benchmarks). CachyOS on certain benchmarks may see something like 5-10% in VERY specific areas that probably don't even impact gaming that much, and you'd never register that difference as a user.
Just switch if you like it. It sounds like you have your other data separated already, so just install along side what you have, boot that, and try it out.
Just don't be let down in when there isn't a big performance difference. Also keep in mind that whatever tweaks any other distro has implemented for gaming, you can simply apply to whatever you're running as well. There are no hidden tweaks, fixes, or proprietary knowledge in any of them that you can't also apply to your running install.