who decides to sue

When the creditor hires the collection agency, they call you to get their payment. In case, they are unable to collect on the account, they send it back to the original creditor with a note "unable to collect". The creditor decides depending upon the total amount if suing will be worth. The court costs and attorney fees are very costly. It should cover the costs of filing the case.

When the debt is sold off to the collection agency, they become the current creditor and hence, all decision now rests with them.

ok, makes sense, how do you tell if the debt was sold or if they are trying to collect for the creditor?

One of the easiest ways to tell is to call the original creditor and ask who legally owns the paper and has authority to take payments.
If the paper is sold,they will direct you back to ca