Gekke Breaks it Down CalyxOS vs GraphneOS

Calyx has more focus on functionality and privacy rather than security. On Graphene, security is always priority #1.
For example: Calyx provides MicroG. This means you can talk to Google Play services, though in a better, more privacy-conscious way. MicroG is an open implementation of Google Play Services.

However, MicroG requires signature spoofing: You need to install a fake Google certificate so that it can trick official apps into thinking they're talking to Google Play Services directly. This could technically be abused, though Calyx takes lots of precautions to prevent that. GrapheneOS with its security-first approach, don't deem this worth the risk. So with apps requiring play services you don't get push messages and network-based location checks, among others.

So, do you want an all round phone to use everyday (and use things like Uber, Facebook, etc) but more private and secure than AOSP, take Calyx. Do you want security over everything and are willing to compromise a bit on functionality and app compatibility (some apps will refuse to run without google play), pick Graphene.

Either way you'll need a Google Pixel by the way.