The 737 NG is a newer aircraft than the A320 and benefits from a more advanced wing design, that’s why it is faster, and can fly at higher altitude than the Airbus.
Launched almost 10 years after the A320, the 737 NG was designed to have lower operating costs than the Airbus. On typical routes, the documented cash operating costs are almost 4% lower than the A320 and the documented maintenance costs are up to the 35% lower on the 737NG.
The cargo hold is bigger on the 737NG and is accessible without ground equipment, which enable the operators to add last minute bags without delaying the flight and enable them to unload/load the plane faster when belt loaders are either not available or quickly available, a common occurrence at peak times or on small airports.
The ability to be turned around more quickly on average than the A320 is due to its superior reliability, ease of maintenance (the plane is much simpler to service & maintain and its lower stance make it more accessible). The speed of boarding is the same on both aircrafts given that the aisles don’t enable 2 passengers to cross each other anyway and one passenger has the ability to block the aisle on both the A320 & the 737 (contrary to a wide body jet).
The slightly larger A320 fuselage has however a negative impact on aerodynamic drag and weight & the higher position of the floor makes the A320 window seats less comfortable at elbow & shoulders height due to the curvature of the fuselage
The 737NG is also sturdier than the A320: it is not as easily damaged by ground equipment or by rough runways.