Is there any difference in usage or are they pretty much interchangeable?
倒産 means "to go bankrupt", that is they can't keep the company in existence because of the company's debts.
If a company go bankrupt, there are three ways that the company's creditors can deal with the company after that.
One of them is 破産. A bankrupt company's all assets are exchanged to money and they are divided among the company's creditors. And the company can't exist.