GOS creates a complete bunker of a phone that can provide defense against pretty much all but the most dedicated state level actors. If you're worried that someone would steal your phone
specifically to target you, Graphene will protect against that. Securitywise it's hard to argue against them, although GOS tends to sacrifice usability in favor of security, which leads to odd decisions. Their device depreciation timeline is also pretty aggressive and really just matches that of the Pixel. (You're also buying the Google phone... to not want Google in your life; this bizarre paradox will always be strange). It's not exactly a recommendation for long-term support. Worth noting however is that usage of GOS is also seen as a signal in and of itself for the authorities that you may have something unsavory to hide, so using it stands out in that regard; some law enforcement officers (I think it was in Spain?) have said that the OS is popular with organized crime. GOS obviously denies the connection and they're probably honest in that the OS isn't deliberately designed for criminals, but it's worth noting at the very least. (Basically GOS is the paradox where someone trying their hardest to be anonymous ends up standing out way too much from the crowd and drawing attention to themselves.)
/e/OS (and similar "non-LineageOS" ROMs really) instead focus more on de-Googling. They're still generally security focused, but the priority is less "someone's after you" and more "corporate surveillance is kinda scary innit". The aim is less to avoid someone actively trying to drain your phone of data and more to prevent your phone from passively sending everything it can possibly find to the Big G's ad machine (as well as whatever other trackers get snuck into apps.) Because of this, they usually have better depreciation timelines and support a lot more devices compared to GOS who only support the Pixel line (which is an increasingly awful set of phones truth be told); their scope is much smaller.
Finally, it's worth noting that the GOS community is absurdly toxic to anyone doing anything privacy-related that isn't under the banner of GOS. It's extremely maximalist, tends to get very upset at other projects whenever they get attention (see sibling reply to this, where they pretty much melted down because an outlet dared to recommend a Fair phone+/e/OS) and the projects official channels have generally encouraged this sort of behavior. It doesn't really damage the software itself, but it's worth considering.
/e/OS (and similar "non-LineageOS" ROMs really) instead focus more on de-Googling. They're still generally security focused, but the priority is less "someone's after you" and more "corporate surveillance is kinda scary innit". The aim is less to avoid someone actively trying to drain your phone of data and more to prevent your phone from passively sending everything it can possibly find to the Big G's ad machine (as well as whatever other trackers get snuck into apps.) Because of this, they usually have better depreciation timelines and support a lot more devices compared to GOS who only support the Pixel line (which is an increasingly awful set of phones truth be told); their scope is much smaller.
Finally, it's worth noting that the GOS community is absurdly toxic to anyone doing anything privacy-related that isn't under the banner of GOS. It's extremely maximalist, tends to get very upset at other projects whenever they get attention (see sibling reply to this, where they pretty much melted down because an outlet dared to recommend a Fair phone+/e/OS) and the projects official channels have generally encouraged this sort of behavior. It doesn't really damage the software itself, but it's worth considering.