Client's transaction context is important always.
A..If the client has a transaction context, it means he wants the process to be transactional - atomic principle applied, all or nothing
B..if the client does not have a transaction context, then it's quite possible that the client does not mind the atomicity of the proccess.
For A, a method with the REQUIRES_NEW transaction attribute will NOT mark the client's transaction for roll back if an exception happens, system exceptions and application exceptions marked to achieve a rollback, because the transaction running is not the client's one. The new transaction will be rolled-back but the client's transaction will continue. REQUIRED attribute will mark the client's transaction for rollback because the method will run using the client's transaction and thus it will be affected directly.
For, B, No client's transaction context means on the client's perspective nothing will be marked for rollback because there is no transaction to talk about. The client will not even know that there are transactions, if any, running behind the scenes.