Selfhosted

Why not get both (free teir on Plex), and decide for yourself?

If you want another opinion from an internet stranger though:

tl;dr: Plex if want simple seamless integration, and are prepared to spend money.

Jellyfin if you want FOSS, but are prepared to spend time.

I run both Jellyfin and Plex, and I only use Plex. It's more polished, has more clients, and has less bugs than Jellyfin. Plus, there are more community applications that are built around Plex vs Jellyfin.

For example, if you want to share your Jellyfin server, you have to manually forward ports, setup DNS records, dynamic DNS services, maybe reverse proxying, just to get easy access outside your network. Meanwhile, Plex is more or less plug and play (you might need to forward a port if the automatic port forward doesn't work)

That being said, I have the lifetime Plex Pass, and I don't think the monthly subscription for Plex is worth it.

I have a ton of friends that use my Jellyfin server instead of Plex, just because the Jellyfin mobile apps are free, so I keep Jellyfin running even though I don't personally use it.

If you decide to go with Plex, I would highly recommend getting the lifetime pass instead of a subscription.