Omarchy is focused mainly on ease of use/installation and is built exclusively around Hyperland. CachyOS on the other hand doesn't default to any particular WM/DE - in fact there are a dozen or so options when you install, so you need to be at least a little bit familiar with them and the pros/cons. Same with the package selection, the CachyOS installer ticks a lot of boxes which may not be relevant to you, so you need to take the time to review the selection and untick ones that you don't need. Some package names may not be obvious to you, so you'd need to google it and see if that's something you want. So there's a bit of a technical barrier there.

Also, CachyOS is focused mostly on performance - providing a highly optimised kernel (ThinLTO/AutoFDO etc), with a custom scheduler (BORE), and CPU-family specific binaries targetting x86-64-v3, v4, and znver4+ families, which are served from their own repos. They also often include upcoming patches into their kernel and other programs if they think it brings in worthy new features/performance benefits. Like how they included support for the new ntfsplus driver before it was mainlined. Overall, it is generally considered to be the fastest performing distro on modern hardware, even more so if you've got AMD (thanks to the znver4+ support).

So the two are very different, with different goals and different approaches, and even differences to the packages, configs and tweaks they serve.

On omarchy it's one and one