GrapheneOS user here – for many years and several devices. Also had many devices, prior to that, running LineageOS.

GrapheneOS

First thing to weigh, between your two options, is that GrapheneOS is considered its own mobile operating system at this point, and the development of this mobile operating system is driven chiefly by privacy and security. While founded on AOSP, GrapheneOS gets such benefits as – but not limited to – more frequently updated kernel patches, code removal or alteration to abate zero-day vulnerabilities normally addressed more slowly (or not at all) in vanilla Android, the security of a re-locked bootloader (only available on Pixel devices), an isolated and sandboxed Google Play to access normal apps (microG and other replacements are considered, in GrapheneOS circles, less secure), isolated user profiles for different sets of apps that have the ability to push notifications to each other, hardened memory allocation, and so much more.

Pixel hardware is a great fit for GrapheneOS due to the kind of security chipsets they employ, too. By selecting a device that allows users to re-lock the bootloader (other devices do not afford this), as well as leverage Pixel-specific hardware-level security features, there’s a measure of consistency for overall security provided to GrapheneOS users and developers, alike. The devs don’t have to provide workarounds, for example, in the same way other ROM makers do, such as for LineageOS. There can be focus. And that benefits everyone who is primarily interested in privacy and security in a phone OS.

LineageOS

Second thing to weigh, between your two options, is the intent behind LineageOS: it’s an open source variation of AOSP, and is considered both an excellent extension mechanism for aging Android devices and an open source alternative to vendor-created – and often vendor-locked – ROMs that come, by default, on a variety of devices. LineageOS has been focused on being one of the most consistent, open source ROMs around. This means the consistency in UX, features, and flexibility of LineageOS can translate between many targeted devices. Over 20 vendors of devices benefit from the hard work of LineageOS.

Like GrapheneOS is focused on privacy and security for their users, LineageOS is focused on being a solid, consistent ROM for their users.

Further Consideration

I can go into the weeds of both, but at some point I made a decision to buy into the Pixel ecosystem – and subsequently learned about GrapheneOS as an option. I value what they offer, and I understand their stricter alignment with their approach to developing an OS. While I choose to lock myself into the Pixel lineup of phones, I would also consider LineageOS – modified to my own specs – if I had to shift to another device. Each have their strengths. Each have their focuses.