Current Nostr DMs are leaking a lot of metadata, basically you can see everything except the actual content. You can see who's DMing who and how often, etc.

There is a new proposal for DMs in the works, and if that's deemed solid, it should be much better.

Just found this, if you want to deep dive into this stuff: https://gist.github.com/staab/f8284af12450dbbdcead6e0c3ed95e2c