I just half went down this rabbit hole, I'm thinking forgejo is the best option (for me) because:

• they dogfood (they actually use their own product, on the other hand gitea uses github and github actions). This makes me feel more confident in forgejo.
• is not "owned" by a for-profit entity that could change course in the future, creating a big hassle for me down the line if I need to swap to something else for whatever enshitified reason (since forgejo is no longer compatible with gitea).
• forgejo seems to be more at-the-ready for finding and fixing security vulnerabilities in their own app (as proclaimed on their site).
• future possibility for federation (gitea is not planning this according to forgejo site).

Forgejo explaining the differences: https://forgejo.org/compare-to-gitea/

For anyone already using gitea though (like yourself), I don't know of any obvious benefits of swapping over to forgejo right now, unless you have experienced bad stability or issues with gitea firsthand.

If I was to choose for a first install, forgejo seems like the better candidate in my books. Mostly because I can be more sure that in a couple years I wont have to change ship to a new product (incase a for-profit company were to add features that aren't in my best interest).

All the reasons that others mentioned, plus it sound cool.