GrapheneOS claims to be a lot more secure, having additional hardening. See https://eylenburg.github.io/android_comparison.htm - keep in mind that it is not an independent comparison, the Graphene guys directly feed what this table is supposed to say in the issue tracker, https://github.com/eylenburg/eylenburg.github.io/issues/. But it gives a good representation of the state of the ROMs according to Graphene.
In regular use, main difference will be that /e/OS comes with access to the alternative cloud service that project provides. It uses the default FOSS solution microG for google api compatibility, unlike GrapheneOS with their sandbox approach. /e/OS sets on AppLounge to install and upgrade both play store or F-Droid apps. Graphene has a small curated app repo instead.
I'd never use GrapheneOS since I don't trust the project. /e/OS is also not my favorite since it feels like it is developing slowly, having had issues with outdated software versions - though it does work well in practice. Have a look at iode for an alternative.
> GrapheneOS claims to be a lot more secure
That's not just a claim, this is an objective fact. GrapheneOS has a excellent track record when it comes to security, they have made several patches that got upstreamed to Android, etc.
/claims/
> I'd never use GrapheneOS since I don't trust the project
Fair enough, you choose what you trust.
But personally, I have never seen a technical claim from GrapheneOS that was wrong or misleading. But I have seen many claims from /e/OS that were technically wrong or misleading. So I trust GrapheneOS more.
Then there is the drama, and all sides annoy me when they behave like this. But I have seen drama coming from all sides.