What are the security trade-offs between Organic Groups and other methods?
It sounds like you are going to need to use Domain Access and set your organic group permissions to fit your use case.   

Here are key points to Multisite vs. Domain Access.

Multisite
 - One database/prefix per site, possible to share users, tables but requires tweaking.
 - Separate install for each but can share modules and themes

Domain access 
 - Single Database
 - shared content, users