In the Company Law: Why does a branch company not have the legal person status, while a subsidiary company has the legal person status?

Because the branch is not a company, it is a branch of the head office. It is not independent in law and economy, but a subsidiary of the head office. A branch company has no name, articles of association or property, and it shall bear legal liability for the debts of the branch company with the assets of the head office.

The subsidiary is a company, and the company certainly has legal personality. The parent company is only its shareholders.