LineageOS has far, far better device compatibility and is focused on that, GrapheneOS is more secure and private and is focused entirely on security.

LineageOS is just the Android Open Source Project core but more stable. Think of it like the bare minimum of Android with some specific features to Lineage, mainly aesthetics. GrapheneOS is focused on security-privacy and changes the kernel and replaces operating system components to higher-security ones.

All of the features in GrapheneOS' feature list don't exist at all on LineageOS: https://grapheneos.org/features because LineageOS is mostly just AOSP.

LineageOS also sometimes connects to Google for things like connectivity checks and connects elsewhere for SUPL/PSDS. GrapheneOS replaces those with their own supl.grapheneos.org etc servers.

LineageOS isn't as centralised, some individual people run and update devices with custom builds rather than LineageOS themselves. Depending on the device you will miss updates. In some cases they also enable userdebug for compatibility, which can be a security weakness since you are able to perform root access.

(Not counting MicroG / Sandboxed Google Play etc since LineageOS typically doesn't bundle it)