Application example from Coilcraft on how coupled inductors gain advantage over separately wound inductors, calculations included. Link here (PDF)
The SEPIC (Single-Ended Primary Inductance Converter) topology is used in applications that require characteristics of both a buck and a boost regulator, specifically the ability to step up and step down the input voltage. Most often operated in CCM (Continuous Conduction Mode), SEPIC provides a non-inverted output voltage.
Typically, SEPIC is used in battery operated systems and automotive applications. In these applications, the battery input voltage, or bus line voltage, may be greater or less than that of the desired output voltage, depending on the charge state of the battery. The SEPIC topology can operate over more of the battery discharge cycle because of the ability to regulate the output voltage over a wider input voltage range, including above and below the output voltage.
The selection of one coupled inductor over two single parts saves board space and can also save cost.