Turret gear scales less than linearly with barrel size, so quad turrets are more compact and cheaper than twice the number of twin turrets.
One turret can shoot down multiple missiles in a salvo, but against numerous small salvos number of fire controls may be the limiting factor - bigger turrets than required to destroy one salvo give no benefit because you can't split them between fire controls.
Also, sophisticated Gauss turrets are expensive, a quad turret may cause some concern for maintenance. It's good practice to have more MSP than your Max Repair value to avoid random breakdowns before your supplies run low, and more than twice your Max Repair value is beneficial because it means field repairs are possible. Quad turrets may force you to run additional engineering spaces to match these break points or your desired maintenance life.
I prefer to err on the side of large, efficient components and the engineering overhead to make them work, but it's something to be aware of.