This is not possible with just connected accounts.
Only registered users with moderator permissions at site A can moderate site A, only registered users with moderator permissions at site B can moderate site B.
This is not possible with just connected accounts.
Only registered users at site A can buy upgrades at site A, only registered users at site B can by upgrades at site B.
This is not possible with just connected accounts.
Only users that are logged into site A are logged into site A, only users that are logged into site B are logged into site B.
What connected accounts does offer:
If a user that is registered at site A comes to site B (where he is currently not registered) he can register there without having to choose a password and go through email validation (if required).
When he visits site B afterwards without being logged in there he can log in via site A - if he is logged in at site A at this point it's just a click to log into site B.