Forgejo is where the dev is happening now.

Gitea is developed by a corporation. If you trust corporations not to enshittify eventually, maybe Gitea will be the exception to the rule, but I doubt it, for sufficiently long definitions of "eventually". Forgejo was forked specifically because the governance needed to be detached from the corporation, and that wasn't going to happen with Gitea. The community of open-source developers mostly voted with their feet. Forgejo is, in my humble opinion, going places. Gitea is not. Nothing specifically wrong with it, per se, but it doesn't really offer a sustainable development path forward I don't think.

It’s a fork of Gitea with more extensive development.

Forked from gitea. The owners of the project implemented a change to the pr system where by you had the sign an agreement that the code belonged to them. This was seen as an intent to relisense at some point. Devs that wanted it to stay open moved to forgejo.

Until recently you could swap forgejo in to your gitea data, but now they are incompatible due to divergence.

I didn't notice a difference. Maybe if you start new then go forgejo but existing gitea I see no reason to move.