It's really only between Anthropic and OpenAI for many of my use cases, since I have a Zero Data Retention agreement with both. I'm not trusting random inference providers and especially not Elmo with sensitive data.
plenty of companies offer ZDR and are just as random as OpenAI and Anthropic in their age
You do not have a ZDR with Anthropic.
For Mythos and even Fable they require prompt retention on their end.
edit: or more precisely if you want to access Mythos/Fable ZDR does not apply, and depending on config the exclusion can affect other models.
or Tinfoil [0]? They serve open models with container integrity attested by Nvidia/AMD enclaves. Every cloud provider offers this of course, but not usually in a way that can be shared between distrusting users for economical inference. It still relies on the open-source containers being secure, and there's probably hardware sidechannels and stuff, but personally (ie privacy not liability) I trust it more than a contract
[0] https://tinfoil.sh