Both can satisfy the requirement for a qualifying parent, branch, subsidiary, or affiliate relationship, so the choice is usually driven by tax, liability, and administration. What matters for the classification is that the chosen relationship genuinely exists, is documented, and that the organisation is doing business on both sides.
Choose for the business, document for the file
Make the structural decision with corporate and tax advisers, then treat the immigration question as whether the resulting relationship can be proved. A subsidiary needs incorporation records and evidence of control; a branch needs registration showing the foreign entity itself carrying on business. Either way the applicant's proposed duties must still be primarily managerial or executive, which is a separate question the structure does not answer.
Make the structural decision with corporate and tax advisers, then treat the immigration question as the narrower one: can the resulting relationship be proved. A subsidiary needs incorporation records and evidence of who controls the shares; a branch needs registration showing the foreign entity itself carrying on business. Either way both entities must be doing business, and the applicant's proposed duties must still be primarily managerial or executive, which the structure does not answer.
Add the requirement of one continuous year of qualifying employment with the organisation abroad within the preceding three years, and note that a new-office approval is limited to one year initially, with the extension judged against implementation.