Graphene only works on Pixel phones. Graphene is more private and secure, but might be too many issues for people who do not care about such things that much. Lineage has better support for different phone models, and you can make it just like a normal Android OS, that just happens to provide updates for your phone years after the manufacturer stops sending them.

Neither of them is better than the other, it's just about your priorities. Get Graphene if you have a Pixel and you value privacy and are willing to tinker with it a bit if some apps don't work.

Lineage covers many devices but is not very privacy friendly. It does not include Google integration by default. The ßain advantage is longer software support.

Graphene is most secure and privacy friendly OS and comes with support for sandboxed GApps (optional). Unfortunately it is only made for Google Pixel devices so I'm out.

Depending on your reasons and device you could also check alternatives like /e/.

I use graphene because I just like its way stricter security features, such as randomized numbers on the keypad when unlocking and it not having any Google services by default

But if you dont care about that and you would rather use MicroG (which is a little project that still runs at root access, but dosent send as much data to google) instead of G services just being sandboxed you can just as well use linaege

Also, linaege is a Team of volunteers that maintain many phones, as grapheneOS only makes Roms for the Google Pixel Series, so all their effort is towards the pixel phones. But as far as I know Graphene only maintains the Roms for phones that are still maintained by Google themselves, only giving a year or so extended support, but I dont know how long the Maintainer(s) that support the Pixels will maintain the Rom

Graphene has a bunch of features that you may or may not agree contribute to privacy over all (funny since it only operates on Google's devices, that is, devices designed by a US enterprise).

LineageOS has some little QoL features but otherwise keeps it very AOSP. The most prominent difference is the dependence on specific device maintainers, meaning that some devices may get stuck on A13 while others may already have A14 or 15, though imo it's a small price to pay for having a modern OS on a 10 y/o phone or tablet. Graphene only provides support for Pixel models that have security updates, so you will end up with LOS if you'd like to keep using your Pixel 2/3/4 etc.

LOS can get rid of the pill at the bottom of the screen 😏