What are the differences between using circular type air ducts and rectangular type air ducts?

Circular ducts have less resistance to flow, and with less noise because most of them comes with pre insulation from the inside. Fittings and ducting are more expensive, more strength since they are wire reinforced from the outside. Rectangular ducts are less expensive, has more resistance to flow, should be within the duct aspect ratio, within a duct specific gage thickness, and consumes less space compared to circular ducts.

Circular type is best in terms of minimizing hydraulic losses as the square or rectangular shapes have sharp edges at the corners where separation occurs.

Square is next to come and least the rectangular, but why we use rectangular is because we are forced for a maximum height to allow the allowance of insulation and clearance from false ceiling, so say you have a maximum height of 12 inch, so first you should consider a circular duct and check flow rate, if it's less than what you want, then try the square one, if the same problem happens and you still need more area to get more flow rate, then use the rectangular one.

but make sure as recommended that aspect ratio (Width over height) should not exceed 4 or 5, afterwards you will have much noise and more friction losses.

Don't forget to check outcome noise according to the application or the building.

Circular ducts are very much advantageous compared to rectangular ducts with much of specific reasons.

Circular Ducts have less friction and more efficient airflow besides faster installaton, lower initial cost , less noise pollution where as rectangular air duct acquires back position in comparison of all these specialities.

Rectangular ducts have some advantages over circular ducts when it comes to rectangular ducts solely like better for low pressure systems, easily connects fan coil to main duct, nad takes up less height.

Each has advantages and disadvantages over each other but when compared circular has more advantages and less disadvantages over rectangular ducts.

Rectangular ducts have more airflow compared to circular ducts and are cheaper to manufacture. Think about it, we just need bolt the sheet metal to for a rectangular cross section instead of needing to do spiral ductwork.

Circular ducts are 'stronger' than rectangular ducts and as the other guy said, also has better aesthetics which is why it is often used in exposed areas.

when the site is open ceiling condition, the circular ducts can be used. because we have no BOFC. it is mainly for aesthetic look. but in false ceiling sites we have to design the duct as per given duct area (area between true ceiling and false ceiling).so we choose rectangular type duct. In rectangular type we can adjust the height and width of duct. but we can't adjust the diameter.