What is the difference that exists between setting up a Subsidiary company and setting up a Branch Office?

You can set up a subsidiary as a separate entity, but you cannot do the same with a Branch Office.
The Subsidiary Company is taxed the same as any Hong Kong resident company, while a Branch Office is charged a similar corporate income tax rate.
The subsidiary follows guidelines for the annual submission of financial statements just like the local companies, while a branch has fewer accounting and reporting requirements.
The Subsidiary Company can do much more business activities that the parent company while the Branch Office must do similar business activities as the parent company.