(Tailscale founder here) Two main differences: first, every DERP server used by your tailnet must be accessible by every node on your tailnet at all times, otherwise you get hard-to-debug netsplits. That's a very high bar to maintain so we've historically recommended you don't try. In contrast, peer relays are "if a given pair of nodes can connect through any of the relays, go for it" so deploying one is always a performance and reliability improvement.

Secondly, peer relays support UDP while DERP is TCP-only. That would be fixable by simply improving the DERP protocol, but as we explored that option, we decided to implement the Peer Relay layer instead as a more complete solution.

Talking out my ass, but as with all things Tailscale, not much, aside from easier to use / less manual setup.

Nothing they do was impossible before, but their big win is making world wide private networking easy and accessible.

I’ve been on-boarding my friends who have their own local media servers setup so we can all share/stream content from each other.