Tough question to answer in detail.

Both strive to address the centralisation issue with today’s social media and their control, moderation and censorship.

Nostr is based on using a single defined fragment of data called an event. Everything in Nostr is an event. Different kinds exist, allowing different use cases - like a user profile, contact lists, reactions, login, etc. No one can stop you joining or using the protocol (no invite needed). Data is hosted by dumb relays that allow data redundancy and resilience against single point of failure (and event multi-point) censorship. However if you want the data to be hosted forever, you’ll likely need to self host or pay for one or more relays. Your identity is your self-derived keys.

Bluesky seems to be a federated Mastadon model that attempts to have community hub servers that still host all your content - so you hope they don’t just ban you one day. It’s a complex AT protocol with lots of different formats and sub-protocols. It doesn’t appear to use cryptography effectively - the server owns your secret/private keys on your behalf. It’s also developed by a company as opposed to an open community.